80 results found for "real zero" in Class 10.
Question
Hard Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 27
यदि (p(x)=x-2 +2\sqrt{5}x+5), तो इसका वास्तविक शून्यक क्या है?
If (p(x)=x-2 +2\sqrt{5}x+5), what is its real zero?
#repeated-zero
#perfect-square
#irrational
A \(-\sqrt{5}\) दो बार / \(-\sqrt{5}\) twice
B \(\sqrt{5}\) दो बार / \(\sqrt{5}\) twice
C (5) दो बार / (5) twice
D कोई वास्तविक शून्यक नहीं / No real zero
Explanation opens after your attempt
Correct Answer
A. \(-\sqrt{5}\) दो बार / \(-\sqrt{5}\) twice
Step 1
Concept
(p(x)=\(x+\sqrt{5}\)2 ), so the zero is \(-\sqrt{5}\) twice. A perfect-square form gives a repeated zero.
Step 2
Why this answer is correct
The correct answer is A. \(-\sqrt{5}\) दो बार / \(-\sqrt{5}\) twice. (p(x)=\(x+\sqrt{5}\)2 ), so the zero is \(-\sqrt{5}\) twice. A perfect-square form gives a repeated zero.
Step 3
Exam Tip
(p(x)=\(x+\sqrt{5}\)2 ), इसलिए शून्यक \(-\sqrt{5}\) दो बार है। पूर्ण वर्ग रूप से दोहराया शून्यक मिलता है।
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Question
Hard Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 27
किस बहुपद के शून्यक वास्तविक हैं लेकिन परिमेय नहीं हैं?
Which polynomial has real zeroes but not rational zeroes?
#real-irrational-zeroes
#identification
#mcq
A \(x^2-9\)
B \(x^2+9\)
C \(x^2-8\)
D \(x^2-6x+9\)
Explanation opens after your attempt
Correct Answer
C. \(x^2-8\)
Step 1
Concept
From \(x^2-8=0\), \(x=\pm2\sqrt{2}\), which are irrational real. Check both perfect-square status and positivity.
Step 2
Why this answer is correct
The correct answer is C. \(x^2-8\). From \(x^2-8=0\), \(x=\pm2\sqrt{2}\), which are irrational real. Check both perfect-square status and positivity.
Step 3
Exam Tip
\(x^2-8=0\) से \(x=\pm2\sqrt{2}\), जो अपरिमेय वास्तविक हैं। पूर्ण वर्ग और धनात्मकता दोनों जाँचें।
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Question
Hard Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 28
यदि (p(x)=x-2 -2) है, तो इसके वास्तविक शून्यकों के बारे में सही कथन कौन सा है?
If (p(x)=x-2 -2), which statement about its real zeroes is correct?
#polynomials
#irrational-numbers
#real-zeroes
A दोनों परिमेय हैं / Both are rational
B दोनों अपरिमेय हैं / Both are irrational
C एक परिमेय और एक अपरिमेय है / One is rational and one is irrational
D कोई वास्तविक शून्यक नहीं है / No real zero exists
Explanation opens after your attempt
Correct Answer
B. दोनों अपरिमेय हैं / Both are irrational
Step 1
Concept
The zeroes are \(x=\pm\sqrt{2}\), and \(\sqrt{2}\) is irrational. In exams, simplify square-root zeroes before deciding the type.
Step 2
Why this answer is correct
The correct answer is B. दोनों अपरिमेय हैं / Both are irrational. The zeroes are \(x=\pm\sqrt{2}\), and \(\sqrt{2}\) is irrational. In exams, simplify square-root zeroes before deciding the type.
Step 3
Exam Tip
शून्यक \(x=\pm\sqrt{2}\) हैं और \(\sqrt{2}\) अपरिमेय है। परीक्षा में वर्गमूल वाले शून्यकों को सरल करके जाँचें।
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Question
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
किसी द्विघात बहुपद का ग्राफ (x)-अक्ष को नहीं छूता। उसके विविक्त वास्तविक शून्यकों की संख्या क्या होगी?
A quadratic polynomial graph does not touch the (x)-axis. What is the number of distinct real zeroes?
#quadratic
#no-intersection
#real-zeroes
A शून्य / Zero
B एक / One
C दो / Two
D अनंत / Infinite
Explanation opens after your attempt
Correct Answer
A. शून्य / Zero
Step 1
Concept
For a real zero the graph must meet the (x)-axis. No meeting means no real zero.
Step 2
Why this answer is correct
The correct answer is A. शून्य / Zero. For a real zero the graph must meet the (x)-axis. No meeting means no real zero.
Step 3
Exam Tip
वास्तविक शून्यक के लिए ग्राफ का (x)-अक्ष से मिलना जरूरी है। कोई मिलन नहीं तो कोई वास्तविक शून्यक नहीं।
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Question
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
स्थिर बहुपद (p(x)=5) के ग्राफ के वास्तविक शून्यक कितने हैं?
How many real zeroes does the constant polynomial (p(x)=5) have?
#constant-polynomial
#no-zero
#graph
A शून्य / Zero
B एक / One
C पाँच / Five
D अनंत / Infinite
Explanation opens after your attempt
Correct Answer
A. शून्य / Zero
Step 1
Concept
The line (y=5) is parallel to the (x)-axis and does not meet it. So it has no real zero.
Step 2
Why this answer is correct
The correct answer is A. शून्य / Zero. The line (y=5) is parallel to the (x)-axis and does not meet it. So it has no real zero.
Step 3
Exam Tip
रेखा (y=5) (x)-अक्ष के समानांतर है और उससे नहीं मिलती। इसलिए कोई वास्तविक शून्यक नहीं है।
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Question
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि परवलय नीचे की ओर खुलता है और (x)-अक्ष को दो बिंदुओं पर काटता है तो वास्तविक शून्यकों की संख्या क्या होगी?
If a parabola opens downward and cuts the (x)-axis at two points, how many real zeroes will it have?
#parabola
#downward
#real-zeroes
A दो / Two
B एक / One
C शून्य / Zero
D चार / Four
Explanation opens after your attempt
Step 1
Concept
The opening direction alone does not decide the number of zeroes. Two intersections clearly give two real zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो / Two. The opening direction alone does not decide the number of zeroes. Two intersections clearly give two real zeroes.
Step 3
Exam Tip
खुलने की दिशा शून्यकों की संख्या अकेले तय नहीं करती। दो कटान स्पष्ट रूप से दो वास्तविक शून्यक देते हैं।
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Question
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि किसी द्विघात बहुपद के ग्राफ का शीर्ष (x)-अक्ष पर है तो वास्तविक शून्यकों के बारे में क्या सही है?
If the vertex of a quadratic polynomial graph lies on the (x)-axis, what is correct about its real zeroes?
#vertex
#equal-zeroes
#quadratic
A दोनों वास्तविक शून्यक समान हैं / Both real zeroes are equal
B दोनों वास्तविक शून्यक भिन्न हैं / Both real zeroes are distinct
C कोई वास्तविक शून्यक नहीं है / There is no real zero
D तीन वास्तविक शून्यक हैं / There are three real zeroes
Explanation opens after your attempt
Correct Answer
A. दोनों वास्तविक शून्यक समान हैं / Both real zeroes are equal
Step 1
Concept
When the vertex lies on the (x)-axis, the parabola touches the axis at one point. Hence the zeroes are equal.
Step 2
Why this answer is correct
The correct answer is A. दोनों वास्तविक शून्यक समान हैं / Both real zeroes are equal. When the vertex lies on the (x)-axis, the parabola touches the axis at one point. Hence the zeroes are equal.
Step 3
Exam Tip
शीर्ष (x)-अक्ष पर होने पर परवलय अक्ष को एक ही बिंदु पर छूता है। इसलिए शून्यक समान होते हैं।
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Question
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
एक बहुपद का ग्राफ (x)-अक्ष को ((-5,0)) पर काटता और ((2,0)) पर छूता है। उसके वास्तविक शून्यकों की संख्या क्या है?
A polynomial graph cuts the (x)-axis at ((-5,0)) and touches it at ((2,0)). What is the number of real zeroes?
#touch-cross
#real-zeroes
#graph
A दो / Two
B एक / One
C तीन / Three
D शून्य / Zero
Explanation opens after your attempt
Step 1
Concept
The two different (x)-values (-5) and (2) are zeroes. Touching also gives a zero.
Step 2
Why this answer is correct
The correct answer is A. दो / Two. The two different (x)-values (-5) and (2) are zeroes. Touching also gives a zero.
Step 3
Exam Tip
दो अलग (x)-मान (-5) और (2) शून्यक हैं। छूना भी शून्यक देता है।
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Question
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि द्विघात ग्राफ (x)-अक्ष को दो अलग बिंदुओं पर काटता है तो उसके वास्तविक शून्यक कैसे होंगे?
If a quadratic graph cuts the (x)-axis at two distinct points, what kind of real zeroes does it have?
#quadratic
#distinct-real-zeroes
#graph
A दो भिन्न वास्तविक शून्यक / Two distinct real zeroes
B दो समान वास्तविक शून्यक / Two equal real zeroes
C कोई वास्तविक शून्यक नहीं / No real zero
D एक ही शून्यक और एक काल्पनिक शून्यक / One zero and one imaginary zero
Explanation opens after your attempt
Correct Answer
A. दो भिन्न वास्तविक शून्यक / Two distinct real zeroes
Step 1
Concept
Two separate intersections give two distinct real zeroes. Different (x)-intercepts mean different zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो भिन्न वास्तविक शून्यक / Two distinct real zeroes. Two separate intersections give two distinct real zeroes. Different (x)-intercepts mean different zeroes.
Step 3
Exam Tip
दो अलग कटान दो अलग वास्तविक शून्यक देते हैं। ग्राफ में अलग (x)-प्रतिच्छेद अलग शून्यक होते हैं।
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Question
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि किसी घन बहुपद का ग्राफ (x)-अक्ष को (-1) पर काटता है और (2) पर छूता है तो अलग-अलग वास्तविक शून्यक कितने हैं?
If the graph of a cubic polynomial crosses the (x)-axis at (-1) and touches it at (2), how many distinct real zeroes are there?
#cubic
#distinct-zeroes
#graph
A दो / Two
B तीन / Three
C एक / One
D शून्य / Zero
Explanation opens after your attempt
Step 1
Concept
The distinct zeroes are only (-1) and (2). A touching zero may be repeated but its distinct value is counted once.
Step 2
Why this answer is correct
The correct answer is A. दो / Two. The distinct zeroes are only (-1) and (2). A touching zero may be repeated but its distinct value is counted once.
Step 3
Exam Tip
अलग-अलग शून्यक केवल (-1) और (2) हैं। छूने वाला शून्यक दोहराया हो सकता है पर अलग मान एक ही गिना जाता है।
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Question
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि परवलय (x)-अक्ष से ऊपर ही रहता है और उसे कहीं नहीं छूता तो वास्तविक शून्यकों की संख्या क्या होगी?
If a parabola remains entirely above the (x)-axis and never touches it, how many real zeroes does it have?
#quadratic
#no-real-zero
#parabola
A शून्य / Zero
B एक / One
C दो / Two
D अनंत / Infinite
Explanation opens after your attempt
Correct Answer
A. शून्य / Zero
Step 1
Concept
If the graph does not meet the (x)-axis there is no real zero. Only points with (y=0) are counted.
Step 2
Why this answer is correct
The correct answer is A. शून्य / Zero. If the graph does not meet the (x)-axis there is no real zero. Only points with (y=0) are counted.
Step 3
Exam Tip
ग्राफ (x)-अक्ष से न मिले तो वास्तविक शून्यक नहीं होता। केवल (y=0) वाले बिंदु गिने जाते हैं।
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Question
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि किसी परवलय का शीर्ष ((-14,0)) है और वह नीचे की ओर खुलता है, तो अलग वास्तविक शून्यक कितने हैं?
If the vertex of a parabola is ((-14,0)) and it opens downward, how many distinct real zeroes are there?
#vertex
#tangent
#distinct zero
A शून्य / Zero
B एक / One
C दो / Two
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Step 1
Concept
The vertex lies on the (x)-axis, so the parabola touches at ((-14,0)). Tip: if the vertex has (y=0), there is one distinct zero.
Step 2
Why this answer is correct
The correct answer is B. एक / One. The vertex lies on the (x)-axis, so the parabola touches at ((-14,0)). Tip: if the vertex has (y=0), there is one distinct zero.
Step 3
Exam Tip
शीर्ष (x)-अक्ष पर है, इसलिए परवलय ((-14,0)) पर स्पर्श करेगा। टिप: शीर्ष का (y)-मान (0) हो तो एक अलग शून्यक होता है।
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Question
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=x^{12}+1) है, तो उसके ग्राफ के वास्तविक शून्यकों की संख्या क्या है?
If (p(x)=x^{12}+1), what is the number of real zeroes of its graph?
#even power
#no real zero
#graph
A शून्य / Zero
B एक / One
C दो / Two
D बारह / Twelve
Explanation opens after your attempt
Correct Answer
A. शून्य / Zero
Step 1
Concept
For real (x), \(x^{12}\geq0\), so \(x^{12}+1>0\). Tip: an always positive polynomial does not cut the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. शून्य / Zero. For real (x), \(x^{12}\geq0\), so \(x^{12}+1>0\). Tip: an always positive polynomial does not cut the (x)-axis.
Step 3
Exam Tip
वास्तविक (x) के लिए \(x^{12}\geq0\), इसलिए \(x^{12}+1>0\) है। टिप: हमेशा धनात्मक बहुपद (x)-अक्ष को नहीं काटता।
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Question
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
परवलय (x)-अक्ष को दो बिंदुओं पर काटता है और (y)-अक्ष को ((0,25)) पर काटता है। वास्तविक शून्यकों की संख्या क्या है?
A parabola cuts the (x)-axis at two points and cuts the (y)-axis at ((0,25)). What is the number of real zeroes?
#x intercept
#y intercept
#zero count
A एक / One
B दो / Two
C तीन / Three
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Step 1
Concept
Real zeroes are counted from (x)-axis intersections, not from the (y)-axis intercept. Tip: ((0,25)) does not show a zero.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. Real zeroes are counted from (x)-axis intersections, not from the (y)-axis intercept. Tip: ((0,25)) does not show a zero.
Step 3
Exam Tip
वास्तविक शून्यक (x)-अक्ष कटानों से गिने जाते हैं, (y)-अक्ष कटान से नहीं। टिप: ((0,25)) शून्यक नहीं बताता।
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Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (x)-अक्ष से मिलने वाले बिंदु ((-11,0)), ((-11,0)), ((4,0)), ((4,0)) लिखे हैं, तो अलग वास्तविक शून्यक कितने हैं?
If the points meeting the (x)-axis are written as ((-11,0)), ((-11,0)), ((4,0)), ((4,0)), how many distinct real zeroes are there?
#repeated points
#distinct zeroes
#graph
A एक / One
B दो / Two
C तीन / Three
D चार / Four
Explanation opens after your attempt
Step 1
Concept
Repeated points give the same (x)-values, so the distinct zeroes are (-11) and (4). Tip: count the same (x)-value once.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. Repeated points give the same (x)-values, so the distinct zeroes are (-11) and (4). Tip: count the same (x)-value once.
Step 3
Exam Tip
दोहराए बिंदु समान (x)-मान देते हैं, इसलिए अलग शून्यक (-11) और (4) हैं। टिप: समान (x)-मान को एक बार गिनें।
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Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=(x+2)6 (x-5)2 ) है, तो अलग वास्तविक शून्यकों की संख्या और ग्राफ का व्यवहार क्या है?
If (p(x)=(x+2)6 (x-5)2 ), what are the number of distinct real zeroes and graph behavior?
#even multiplicity
#distinct zeroes
#tangent
A दो, दोनों पर स्पर्श / Two, touches at both
B दो, दोनों पर कटान / Two, crosses at both
C आठ, सभी पर स्पर्श / Eight, touches at all
D एक, केवल (x=-2) पर स्पर्श / One, touches only at (x=-2)
Explanation opens after your attempt
Correct Answer
A. दो, दोनों पर स्पर्श / Two, touches at both
Step 1
Concept
There are two distinct zeroes (-2) and (5), and both have even powers. Tip: at an even-power zero the graph usually touches.
Step 2
Why this answer is correct
The correct answer is A. दो, दोनों पर स्पर्श / Two, touches at both. There are two distinct zeroes (-2) and (5), and both have even powers. Tip: at an even-power zero the graph usually touches.
Step 3
Exam Tip
दो अलग शून्यक (-2) और (5) हैं तथा दोनों की घात सम है। टिप: सम घात वाले शून्यक पर ग्राफ सामान्यतः स्पर्श करता है।
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Question
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी परवलय का शीर्ष ((12,0)) है और वह ऊपर की ओर खुलता है, तो अलग वास्तविक शून्यक कितने हैं?
If the vertex of a parabola is ((12,0)) and it opens upward, how many distinct real zeroes are there?
#vertex
#tangent
#distinct zero
A शून्य / Zero
B एक / One
C दो / Two
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Step 1
Concept
The vertex lies on the (x)-axis, so the parabola touches at ((12,0)). Tip: if the vertex has (y=0), there is one distinct zero.
Step 2
Why this answer is correct
The correct answer is B. एक / One. The vertex lies on the (x)-axis, so the parabola touches at ((12,0)). Tip: if the vertex has (y=0), there is one distinct zero.
Step 3
Exam Tip
शीर्ष (x)-अक्ष पर है, इसलिए परवलय ((12,0)) पर स्पर्श करेगा। टिप: शीर्ष का (y)-मान (0) हो तो एक अलग शून्यक होता है।
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Question
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(x)=x^{10}+1) है, तो उसके ग्राफ के वास्तविक शून्यकों की संख्या क्या है?
If (p(x)=x^{10}+1), what is the number of real zeroes of its graph?
#even power
#no real zero
#graph
A शून्य / Zero
B एक / One
C दो / Two
D दस / Ten
Explanation opens after your attempt
Correct Answer
A. शून्य / Zero
Step 1
Concept
For real (x), \(x^{10}\geq0\), so \(x^{10}+1>0\). Tip: an always positive polynomial does not cut the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. शून्य / Zero. For real (x), \(x^{10}\geq0\), so \(x^{10}+1>0\). Tip: an always positive polynomial does not cut the (x)-axis.
Step 3
Exam Tip
वास्तविक (x) के लिए \(x^{10}\geq0\), इसलिए \(x^{10}+1>0\) है। टिप: हमेशा धनात्मक बहुपद (x)-अक्ष को नहीं काटता।
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Question
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
परवलय (x)-अक्ष को दो बिंदुओं पर काटता है और (y)-अक्ष को ((0,-20)) पर काटता है। वास्तविक शून्यकों की संख्या क्या है?
A parabola cuts the (x)-axis at two points and cuts the (y)-axis at ((0,-20)). What is the number of real zeroes?
#x intercept
#y intercept
#zero count
A एक / One
B दो / Two
C तीन / Three
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Step 1
Concept
Real zeroes are counted from (x)-axis intersections, not from the (y)-axis intercept. Tip: ((0,-20)) does not show a zero.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. Real zeroes are counted from (x)-axis intersections, not from the (y)-axis intercept. Tip: ((0,-20)) does not show a zero.
Step 3
Exam Tip
वास्तविक शून्यक (x)-अक्ष कटानों से गिने जाते हैं, (y)-अक्ष कटान से नहीं। टिप: ((0,-20)) शून्यक नहीं बताता।
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Question
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (x)-अक्ष से मिलने वाले बिंदु ((-7,0)), ((-7,0)), ((2,0)), ((2,0)) लिखे हैं, तो अलग वास्तविक शून्यक कितने हैं?
If the points meeting the (x)-axis are written as ((-7,0)), ((-7,0)), ((2,0)), ((2,0)), how many distinct real zeroes are there?
#repeated points
#distinct zeroes
#graph
A एक / One
B दो / Two
C तीन / Three
D चार / Four
Explanation opens after your attempt
Step 1
Concept
Repeated points give the same (x)-values, so the distinct zeroes are (-7) and (2). Tip: count the same (x)-value once.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. Repeated points give the same (x)-values, so the distinct zeroes are (-7) and (2). Tip: count the same (x)-value once.
Step 3
Exam Tip
दोहराए बिंदु समान (x)-मान देते हैं, इसलिए अलग शून्यक (-7) और (2) हैं। टिप: समान (x)-मान को एक बार गिनें।
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Question
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(x)=(x-1)2 (x+4)4 ) है, तो अलग वास्तविक शून्यकों की संख्या और ग्राफ का व्यवहार क्या है?
If (p(x)=(x-1)2 (x+4)4 ), what are the number of distinct real zeroes and graph behavior?
#even multiplicity
#distinct zeroes
#tangent
A दो, दोनों पर स्पर्श / Two, touches at both
B दो, दोनों पर कटान / Two, crosses at both
C छह, सभी पर स्पर्श / Six, touches at all
D एक, केवल (x=1) पर स्पर्श / One, touches only at (x=1)
Explanation opens after your attempt
Correct Answer
A. दो, दोनों पर स्पर्श / Two, touches at both
Step 1
Concept
There are two distinct zeroes (1) and (-4), and both have even powers. Tip: at an even-power zero the graph usually touches.
Step 2
Why this answer is correct
The correct answer is A. दो, दोनों पर स्पर्श / Two, touches at both. There are two distinct zeroes (1) and (-4), and both have even powers. Tip: at an even-power zero the graph usually touches.
Step 3
Exam Tip
दो अलग शून्यक (1) और (-4) हैं तथा दोनों की घात सम है। टिप: सम घात वाले शून्यक पर ग्राफ सामान्यतः स्पर्श करता है।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि किसी परवलय का शीर्ष ((-5,0)) है तो वास्तविक शून्यकों की अलग संख्या क्या होगी?
If the vertex of a parabola is ((-5,0)), what will be the distinct number of real zeroes?
#vertex
#tangent
#distinct zero
A शून्य / Zero
B एक / One
C दो / Two
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Step 1
Concept
The vertex lies on the (x)-axis, so the parabola touches at ((-5,0)). Tip: if the vertex has (y=0), there is one distinct zero.
Step 2
Why this answer is correct
The correct answer is B. एक / One. The vertex lies on the (x)-axis, so the parabola touches at ((-5,0)). Tip: if the vertex has (y=0), there is one distinct zero.
Step 3
Exam Tip
शीर्ष (x)-अक्ष पर है इसलिए परवलय ((-5,0)) पर स्पर्श करेगा। टिप: शीर्ष का (y)-मान (0) हो तो एक अलग शून्यक होता है।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि (p(x)=x-8 +1) है तो उसके ग्राफ के वास्तविक शून्यकों की संख्या क्या है?
If (p(x)=x-8 +1), what is the number of real zeroes of its graph?
#even power
#no real zero
#graph
A शून्य / Zero
B एक / One
C दो / Two
D आठ / Eight
Explanation opens after your attempt
Correct Answer
A. शून्य / Zero
Step 1
Concept
For real (x), \(x^8\geq0\), so \(x^8+1>0\). Tip: an always positive polynomial does not cut the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. शून्य / Zero. For real (x), \(x^8\geq0\), so \(x^8+1>0\). Tip: an always positive polynomial does not cut the (x)-axis.
Step 3
Exam Tip
वास्तविक (x) के लिए \(x^8\geq0\), इसलिए \(x^8+1>0\) है। टिप: हमेशा धनात्मक बहुपद (x)-अक्ष को नहीं काटता।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि परवलय (x)-अक्ष को दो बिंदुओं पर काटता है और (y)-अक्ष को ((0,18)) पर काटता है तो वास्तविक शून्यकों की संख्या क्या है?
If a parabola cuts the (x)-axis at two points and cuts the (y)-axis at ((0,18)), what is the number of real zeroes?
#x intercept
#y intercept
#zero count
A एक / One
B दो / Two
C तीन / Three
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Step 1
Concept
Real zeroes are counted from (x)-axis intersections, not from the (y)-axis intercept. Tip: ((0,18)) does not show a zero.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. Real zeroes are counted from (x)-axis intersections, not from the (y)-axis intercept. Tip: ((0,18)) does not show a zero.
Step 3
Exam Tip
वास्तविक शून्यक (x)-अक्ष कटानों से गिने जाते हैं (y)-अक्ष कटान से नहीं। टिप: ((0,18)) शून्यक नहीं बताता।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि (x)-अक्ष से मिलने वाले बिंदु ((-5,0)), ((-5,0)), ((4,0)) लिखे हैं तो अलग वास्तविक शून्यक कितने हैं?
If the points meeting the (x)-axis are written as ((-5,0)), ((-5,0)), ((4,0)), how many distinct real zeroes are there?
#repeated point
#distinct zeroes
#graph
A एक / One
B दो / Two
C तीन / Three
D चार / Four
Explanation opens after your attempt
Step 1
Concept
((-5,0)) is repeated, so the distinct zeroes are (-5) and (4). Tip: count the same (x)-value once.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. ((-5,0)) is repeated, so the distinct zeroes are (-5) and (4). Tip: count the same (x)-value once.
Step 3
Exam Tip
((-5,0)) दोहराया गया है इसलिए अलग शून्यक (-5) और (4) हैं। टिप: समान (x)-मान को एक बार गिनें।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि किसी परवलय का शीर्ष ((4,0)) है, तो वास्तविक शून्यकों की अलग संख्या क्या होगी?
If the vertex of a parabola is ((4,0)), what will be the distinct number of real zeroes?
#vertex
#tangent
#distinct zero
A शून्य / Zero
B एक / One
C दो / Two
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Step 1
Concept
The vertex lies on the (x)-axis, so the parabola touches at ((4,0)). Tip: if the vertex has (y=0), there is one distinct zero.
Step 2
Why this answer is correct
The correct answer is B. एक / One. The vertex lies on the (x)-axis, so the parabola touches at ((4,0)). Tip: if the vertex has (y=0), there is one distinct zero.
Step 3
Exam Tip
शीर्ष (x)-अक्ष पर है, इसलिए परवलय ((4,0)) पर स्पर्श करेगा। टिप: शीर्ष का (y)-मान (0) हो तो एक अलग शून्यक होता है।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=x-6 +1), तो उसके ग्राफ के वास्तविक शून्यकों की संख्या क्या है?
If (p(x)=x-6 +1), what is the number of real zeroes of its graph?
#even power
#no real zero
#graph
A शून्य / Zero
B एक / One
C दो / Two
D छह / Six
Explanation opens after your attempt
Correct Answer
A. शून्य / Zero
Step 1
Concept
For real (x), \(x^6\geq0\), so \(x^6+1>0\). Tip: an always positive polynomial does not cut the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. शून्य / Zero. For real (x), \(x^6\geq0\), so \(x^6+1>0\). Tip: an always positive polynomial does not cut the (x)-axis.
Step 3
Exam Tip
वास्तविक (x) के लिए \(x^6\geq0\), इसलिए \(x^6+1>0\) है। टिप: हमेशा धनात्मक बहुपद (x)-अक्ष को नहीं काटता।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि परवलय (x)-अक्ष को दो बिंदुओं पर काटता है और (y)-अक्ष को ((0,-15)) पर काटता है, तो वास्तविक शून्यकों की संख्या क्या है?
If a parabola cuts the (x)-axis at two points and cuts the (y)-axis at ((0,-15)), what is the number of real zeroes?
#x intercept
#y intercept
#zero count
A एक / One
B दो / Two
C तीन / Three
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Step 1
Concept
Real zeroes are counted from (x)-axis intersections, not from the (y)-axis intercept. Tip: ((0,-15)) does not show a zero.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. Real zeroes are counted from (x)-axis intersections, not from the (y)-axis intercept. Tip: ((0,-15)) does not show a zero.
Step 3
Exam Tip
वास्तविक शून्यक (x)-अक्ष कटानों से गिने जाते हैं, (y)-अक्ष कटान से नहीं। टिप: ((0,-15)) शून्यक नहीं बताता।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (x)-अक्ष से मिलने वाले बिंदु ((2,0)), ((2,0)), ((9,0)) लिखे हैं, तो अलग वास्तविक शून्यक कितने हैं?
If the points meeting the (x)-axis are written as ((2,0)), ((2,0)), ((9,0)), how many distinct real zeroes are there?
#repeated point
#distinct zeroes
#graph
A एक / One
B दो / Two
C तीन / Three
D चार / Four
Explanation opens after your attempt
Step 1
Concept
((2,0)) is repeated, so the distinct zeroes are (2) and (9). Tip: count the same (x)-value once.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. ((2,0)) is repeated, so the distinct zeroes are (2) and (9). Tip: count the same (x)-value once.
Step 3
Exam Tip
((2,0)) दोहराया गया है, इसलिए अलग शून्यक (2) और (9) हैं। टिप: समान (x)-मान को एक बार गिनें।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(x)=x-4 +1), तो उसके ग्राफ के वास्तविक शून्यकों की संख्या क्या है?
If (p(x)=x-4 +1), what is the number of real zeroes of its graph?
#quartic
#no real zero
#graph
A शून्य / Zero
B एक / One
C दो / Two
D चार / Four
Explanation opens after your attempt
Correct Answer
A. शून्य / Zero
Step 1
Concept
For real (x), \(x^4\geq0\), so \(x^4+1>0\). Tip: an always positive polynomial does not cut the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. शून्य / Zero. For real (x), \(x^4\geq0\), so \(x^4+1>0\). Tip: an always positive polynomial does not cut the (x)-axis.
Step 3
Exam Tip
वास्तविक (x) के लिए \(x^4\geq0\), इसलिए \(x^4+1>0\) है। टिप: हमेशा धनात्मक बहुपद (x)-अक्ष को नहीं काटता।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी परवलय का ग्राफ (x)-अक्ष को दो बिंदुओं पर काटता है और (y)-अक्ष को ((0,12)) पर काटता है, तो वास्तविक शून्यकों की संख्या क्या है?
If a parabola cuts the (x)-axis at two points and cuts the (y)-axis at ((0,12)), what is the number of real zeroes?
#x intercept
#y intercept
#zero count
A एक / One
B दो / Two
C तीन / Three
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Step 1
Concept
Real zeroes are counted from (x)-axis intersections, not from the (y)-axis intercept. Tip: ((0,12)) is not a zero.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. Real zeroes are counted from (x)-axis intersections, not from the (y)-axis intercept. Tip: ((0,12)) is not a zero.
Step 3
Exam Tip
वास्तविक शून्यक (x)-अक्ष कटानों से गिने जाते हैं, (y)-अक्ष कटान से नहीं। टिप: ((0,12)) शून्यक नहीं है।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी बहुपद के ग्राफ में (x)-अक्ष से मिलने वाले बिंदु ((1,0)), ((1,0)), ((4,0)) लिखे हैं, तो अलग वास्तविक शून्यक कितने हैं?
If the points meeting the (x)-axis on a polynomial graph are written as ((1,0)), ((1,0)), ((4,0)), how many distinct real zeroes are there?
#repeated point
#distinct zeroes
#graph
A एक / One
B दो / Two
C तीन / Three
D चार / Four
Explanation opens after your attempt
Step 1
Concept
((1,0)) is repeated, so the distinct zeroes are (1) and (4). Tip: count the same (x)-value once.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. ((1,0)) is repeated, so the distinct zeroes are (1) and (4). Tip: count the same (x)-value once.
Step 3
Exam Tip
((1,0)) दोहराया गया है, इसलिए अलग शून्यक (1) और (4) हैं। टिप: समान (x)-मान को एक बार गिनें।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी घन बहुपद का ग्राफ (x)-अक्ष को दो अलग बिंदुओं पर छूता और काटता है, तो अलग वास्तविक शून्यक कितने होंगे?
If the graph of a cubic polynomial touches or crosses the (x)-axis at two distinct points, how many distinct real zeroes will it have?
#cubic
#distinct zeroes
#graph reading
A एक / One
B दो / Two
C तीन / Three
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Step 1
Concept
Distinct zeroes are counted from distinct meeting points with the (x)-axis. Tip: degree gives the maximum, but the actual count is read from the graph.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. Distinct zeroes are counted from distinct meeting points with the (x)-axis. Tip: degree gives the maximum, but the actual count is read from the graph.
Step 3
Exam Tip
अलग शून्यक अलग (x)-अक्ष मिलने वाले बिंदुओं की संख्या से मिलते हैं। टिप: घात से अधिकतम संख्या मिलती है, वास्तविक गिनती ग्राफ से पढ़ें।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी द्विघात ग्राफ का शीर्ष ((3,-4)) है और वह ऊपर की ओर खुलता है, तो वास्तविक शून्यकों की संख्या क्या होगी?
If a quadratic graph has vertex ((3,-4)) and opens upward, what will be the number of real zeroes?
#vertex
#quadratic
#real zeroes
A शून्य / Zero
B एक / One
C दो / Two
D तीन / Three
Explanation opens after your attempt
Step 1
Concept
The vertex is below the (x)-axis and the graph opens upward, so it cuts the (x)-axis twice. Tip: check vertex height and opening direction together.
Step 2
Why this answer is correct
The correct answer is C. दो / Two. The vertex is below the (x)-axis and the graph opens upward, so it cuts the (x)-axis twice. Tip: check vertex height and opening direction together.
Step 3
Exam Tip
शीर्ष (x)-अक्ष के नीचे है और ग्राफ ऊपर खुलता है, इसलिए वह (x)-अक्ष को दो बार काटेगा। टिप: शीर्ष की ऊँचाई और खुलने की दिशा साथ देखें।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी बहुपद के ग्राफ पर (x=-2) पर कटान, (x=1) पर स्पर्श और (x=5) पर कटान है, तो अलग वास्तविक शून्यक कितने हैं?
If a polynomial graph crosses at (x=-2), touches at (x=1), and crosses at (x=5), how many distinct real zeroes are there?
#touching
#crossing
#distinct zeroes
A दो / Two
B तीन / Three
C चार / Four
D एक / One
Explanation opens after your attempt
Correct Answer
B. तीन / Three
Step 1
Concept
The graph meets the (x)-axis at three distinct (x)-values. Tip: both touching and crossing give zeroes.
Step 2
Why this answer is correct
The correct answer is B. तीन / Three. The graph meets the (x)-axis at three distinct (x)-values. Tip: both touching and crossing give zeroes.
Step 3
Exam Tip
तीनों अलग (x)-मानों पर ग्राफ (x)-अक्ष से मिलता है। टिप: स्पर्श और कटान दोनों शून्यक देते हैं।
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Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि (p(x)=-(x-1)(x+4)) है तो ग्राफ के वास्तविक शून्यक कौन से हैं?
If (p(x)=-(x-1)(x+4)), what are the real zeroes of the graph?
#negative factor zeroes
A (1) और (-4) / (1) and (-4)
B (-1) और (4) / (-1) and (4)
C (0) और (-1) / (0) and (-1)
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
A. (1) और (-4) / (1) and (-4)
Step 1
Concept
The outside negative sign does not change the zeroes. Tip: solve (x-1=0) and (x+4=0).
Step 2
Why this answer is correct
The correct answer is A. (1) और (-4) / (1) and (-4). The outside negative sign does not change the zeroes. Tip: solve (x-1=0) and (x+4=0).
Step 3
Exam Tip
बाहरी ऋण चिह्न शून्यकों को नहीं बदलता। टिप: (x-1=0) और (x+4=0) हल करें।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि (p(x)=x-2 -12x+36) है तो अलग वास्तविक शून्यक कौन सा है?
If (p(x)=x-2 -12x+36), what is the distinct real zero?
#distinct zero perfect square
A (6)
B (-6)
C (12)
D कोई नहीं / None
Explanation opens after your attempt
Step 1
Concept
It is ((x-6)2 ), so the distinct zero is (6). Tip: identify a repeated zero from a perfect square.
Step 2
Why this answer is correct
The correct answer is A. (6). It is ((x-6)2 ), so the distinct zero is (6). Tip: identify a repeated zero from a perfect square.
Step 3
Exam Tip
यह ((x-6)2 ) है इसलिए अलग शून्यक (6) है। टिप: पूर्ण वर्ग देखकर दोहराया शून्यक पहचानें।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि कोई ग्राफ (x)-अक्ष को ((m,0)) पर छूता है और कहीं और नहीं मिलता तो अलग वास्तविक शून्यकों की संख्या क्या है?
If a graph touches the (x)-axis at ((m,0)) and does not meet it anywhere else, what is the number of distinct real zeroes?
#single touch zero
A शून्य / Zero
B एक / One
C दो / Two
D (m)
Explanation opens after your attempt
Step 1
Concept
One touching point gives one distinct real zero. Tip: touching also means (p(x)=0).
Step 2
Why this answer is correct
The correct answer is B. एक / One. One touching point gives one distinct real zero. Tip: touching also means (p(x)=0).
Step 3
Exam Tip
एक ही स्पर्श बिंदु एक अलग वास्तविक शून्यक देता है। टिप: छूना भी (p(x)=0) है।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि (p(x)=x-2 +x-6) है तो वास्तविक शून्यक कौन से हैं?
If (p(x)=x-2 +x-6), what are the real zeroes?
#quadratic zeroes factor
A (2) और (-3) / (2) and (-3)
B (-2) और (3) / (-2) and (3)
C (1) और (-6) / (1) and (-6)
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
A. (2) और (-3) / (2) and (-3)
Step 1
Concept
(x-2 +x-6=(x+3)(x-2)), so the zeroes are (-3) and (2). Tip: read the signs in the factors carefully.
Step 2
Why this answer is correct
The correct answer is A. (2) और (-3) / (2) and (-3). (x-2 +x-6=(x+3)(x-2)), so the zeroes are (-3) and (2). Tip: read the signs in the factors carefully.
Step 3
Exam Tip
(x-2 +x-6=(x+3)(x-2)) इसलिए शून्यक (-3) और (2) हैं। टिप: गुणनखंडों के चिह्न ध्यान से पढ़ें।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि किसी बहुपद के वास्तविक शून्यक (5), (5), (-1) हैं तो अलग वास्तविक शून्यक कौन से हैं?
If the real zeroes of a polynomial are (5), (5), (-1), what are the distinct real zeroes?
#distinct repeated values
A (5) और (-1) / (5) and (-1)
B केवल (5) / Only (5)
C (5), (5), (-1)
D केवल (-1) / Only (-1)
Explanation opens after your attempt
Correct Answer
A. (5) और (-1) / (5) and (-1)
Step 1
Concept
The repeated (5) is counted only once among distinct zeroes. Tip: make a list of distinct values.
Step 2
Why this answer is correct
The correct answer is A. (5) और (-1) / (5) and (-1). The repeated (5) is counted only once among distinct zeroes. Tip: make a list of distinct values.
Step 3
Exam Tip
दोहराया (5) अलग शून्यक में एक बार ही गिना जाता है। टिप: अलग मानों की सूची बनाएं।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
किस ग्राफ से ठीक दो अलग वास्तविक शून्यक मिलेंगे?
Which graph will give exactly two distinct real zeroes?
#two distinct zeroes
A जो (x)-अक्ष को दो अलग बिंदुओं पर काटे / One that cuts the (x)-axis at two distinct points
B जो (y)-अक्ष को दो बिंदुओं पर काटे / One that cuts the (y)-axis at two points
C जो (x)-अक्ष से ऊपर रहे / One that stays above the (x)-axis
D जो एक ही बिंदु पर (x)-अक्ष को छुए / One that touches the (x)-axis at one point
Explanation opens after your attempt
Correct Answer
A. जो (x)-अक्ष को दो अलग बिंदुओं पर काटे / One that cuts the (x)-axis at two distinct points
Step 1
Concept
Two distinct (x)-axis intersections give two distinct real zeroes. Tip: do not count (y)-axis intersections as zeroes.
Step 2
Why this answer is correct
The correct answer is A. जो (x)-अक्ष को दो अलग बिंदुओं पर काटे / One that cuts the (x)-axis at two distinct points. Two distinct (x)-axis intersections give two distinct real zeroes. Tip: do not count (y)-axis intersections as zeroes.
Step 3
Exam Tip
दो अलग (x)-अक्ष कटान दो अलग वास्तविक शून्यक देते हैं। टिप: (y)-अक्ष कटान को शून्यक न गिनें।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
किस स्थिति में (0) बहुपद का वास्तविक शून्यक होगा?
In which situation will (0) be a real zero of a polynomial?
#origin zero concept
A ग्राफ ((0,5)) से गुजरता है / The graph passes through ((0,5))
B ग्राफ ((0,0)) से गुजरता है / The graph passes through ((0,0))
C ग्राफ ((5,0)) से गुजरता है / The graph passes through ((5,0))
D ग्राफ ((1,1)) से गुजरता है / The graph passes through ((1,1))
Explanation opens after your attempt
Correct Answer
B. ग्राफ ((0,0)) से गुजरता है / The graph passes through ((0,0))
Step 1
Concept
(0) is a zero when (p(0)=0). Tip: passing through the origin shows zero as a zero.
Step 2
Why this answer is correct
The correct answer is B. ग्राफ ((0,0)) से गुजरता है / The graph passes through ((0,0)). (0) is a zero when (p(0)=0). Tip: passing through the origin shows zero as a zero.
Step 3
Exam Tip
(0) शून्यक तब है जब (p(0)=0) हो। टिप: मूल बिंदु से गुजरना (0) शून्यक बताता है।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि (p(x)=x-2 +6x+10) है तो इसके वास्तविक शून्यकों के बारे में कौन सा कथन सही है?
If (p(x)=x-2 +6x+10), which statement about its real zeroes is correct?
#no real zero quadratic
A दो वास्तविक शून्यक हैं / It has two real zeroes
B एक वास्तविक शून्यक है / It has one real zero
C कोई वास्तविक शून्यक नहीं है / It has no real zero
D हर (x) शून्यक है / Every (x) is a zero
Explanation opens after your attempt
Correct Answer
C. कोई वास्तविक शून्यक नहीं है / It has no real zero
Step 1
Concept
It is ((x+3)2 +1), so it is never (0). Tip: an always positive form gives no (x)-axis intersection.
Step 2
Why this answer is correct
The correct answer is C. कोई वास्तविक शून्यक नहीं है / It has no real zero. It is ((x+3)2 +1), so it is never (0). Tip: an always positive form gives no (x)-axis intersection.
Step 3
Exam Tip
यह ((x+3)2 +1) है इसलिए कभी (0) नहीं होता। टिप: हमेशा धनात्मक रूप (x)-अक्ष कटान नहीं देता।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि किसी ग्राफ में (x=1) पर कटान और (x=6) पर स्पर्श है तो अलग वास्तविक शून्यक कितने हैं?
If a graph crosses at (x=1) and touches at (x=6), how many distinct real zeroes are there?
#crossing touching zeroes
A एक / One
B दो / Two
C तीन / Three
D शून्य / Zero
Explanation opens after your attempt
Step 1
Concept
Both crossing and touching show (p(x)=0). Tip: count the distinct (x)-values.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. Both crossing and touching show (p(x)=0). Tip: count the distinct (x)-values.
Step 3
Exam Tip
कटान और स्पर्श दोनों (p(x)=0) बताते हैं। टिप: अलग (x)-मानों को गिनें।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि किसी बहुपद के आलेख पर बिंदु ((-4,0)), ((0,3)), ((2,0)) और ((5,-1)) हैं तो वास्तविक शून्यक कौन से हैं?
If the points ((-4,0)), ((0,3)), ((2,0)) and ((5,-1)) lie on a polynomial graph, which are the real zeroes?
#graph zeroes coordinates
A (-4) और (2) / (-4) and (2)
B (0) और (5) / (0) and (5)
C (3) और (-1) / (3) and (-1)
D सभी (x)-मान / All (x)-values
Explanation opens after your attempt
Correct Answer
A. (-4) और (2) / (-4) and (2)
Step 1
Concept
Zeroes occur where (y=0). Tip: choose only points lying on the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. (-4) और (2) / (-4) and (2). Zeroes occur where (y=0). Tip: choose only points lying on the (x)-axis.
Step 3
Exam Tip
जहाँ (y=0) है वहीं शून्यक मिलते हैं। टिप: केवल (x)-अक्ष पर पड़े बिंदु चुनें।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि किसी बहुपद के वास्तविक शून्यक (2), (2) और (-5) लिखे हैं, तो अलग वास्तविक शून्यक कौन से हैं?
If the real zeroes of a polynomial are written as (2), (2) and (-5), what are the distinct real zeroes?
#repeated distinct zeroes
A (2) और (-5) / (2) and (-5)
B केवल (2) / Only (2)
C (2), (2), (-5)
D केवल (-5) / Only (-5)
Explanation opens after your attempt
Correct Answer
A. (2) और (-5) / (2) and (-5)
Step 1
Concept
The repeated (2) is counted once for distinct zeroes. Tip: do not rewrite the same value for distinct zeroes.
Step 2
Why this answer is correct
The correct answer is A. (2) और (-5) / (2) and (-5). The repeated (2) is counted once for distinct zeroes. Tip: do not rewrite the same value for distinct zeroes.
Step 3
Exam Tip
दोहराया (2) अलग शून्यक में एक बार गिना जाता है। टिप: अलग शून्यक में समान मान पुनः न लिखें।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=x-2 +2x+5) है तो इसके वास्तविक शून्यकों के बारे में सही कथन कौन सा है?
If (p(x)=x-2 +2x+5), which statement about its real zeroes is correct?
#quadratic no real zero
A दो वास्तविक शून्यक हैं / It has two real zeroes
B एक वास्तविक शून्यक है / It has one real zero
C कोई वास्तविक शून्यक नहीं है / It has no real zero
D हर संख्या शून्यक है / Every number is a zero
Explanation opens after your attempt
Correct Answer
C. कोई वास्तविक शून्यक नहीं है / It has no real zero
Step 1
Concept
It is ((x+1)2 +4), which is always positive. Tip: if the value never becomes (0), there is no (x)-axis intersection.
Step 2
Why this answer is correct
The correct answer is C. कोई वास्तविक शून्यक नहीं है / It has no real zero. It is ((x+1)2 +4), which is always positive. Tip: if the value never becomes (0), there is no (x)-axis intersection.
Step 3
Exam Tip
यह ((x+1)2 +4) है जो हमेशा धनात्मक है। टिप: यदि मान कभी (0) न बने तो (x)-अक्ष कटान नहीं होगा।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि किसी बहुपद का आलेख (x)-अक्ष को तीन बार काटता है और एक बार छूता है, तो अलग वास्तविक शून्यकों की संख्या क्या होगी?
If a polynomial graph crosses the (x)-axis three times and touches it once, what is the number of distinct real zeroes?
#multiple intersections zero count
A तीन / Three
B चार / Four
C एक / One
D शून्य / Zero
Explanation opens after your attempt
Correct Answer
B. चार / Four
Step 1
Concept
Each distinct crossing or touching point gives a distinct real zero. Tip: count distinct points.
Step 2
Why this answer is correct
The correct answer is B. चार / Four. Each distinct crossing or touching point gives a distinct real zero. Tip: count distinct points.
Step 3
Exam Tip
हर अलग कटान या स्पर्श बिंदु एक अलग वास्तविक शून्यक देता है। टिप: अलग बिंदुओं को गिनें।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि किसी ग्राफ का केवल एक (x)-अक्ष कटान ((-5,0)) है और वह वहाँ पार करता है, तो वास्तविक शून्यक कौन सा है?
If a graph has only one (x)-axis intersection ((-5,0)) and it crosses there, what is the real zero?
#single intercept zero
A (5)
B (-5)
C (0)
D कोई नहीं / None
Explanation opens after your attempt
Step 1
Concept
The (x)-value (-5) of the intersection point is the zero. Tip: do not change the negative sign.
Step 2
Why this answer is correct
The correct answer is B. (-5). The (x)-value (-5) of the intersection point is the zero. Tip: do not change the negative sign.
Step 3
Exam Tip
कटान बिंदु का (x)-मान (-5) शून्यक है। टिप: ऋण चिह्न को न बदलें।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=x-2 +4x+4) है तो वास्तविक शून्यकों की संख्या कितनी है?
If (p(x)=x-2 +4x+4), how many real zeroes are there?
#perfect square zero graph
A दो अलग / Two distinct
B एक अलग / One distinct
C शून्य / Zero
D चार / Four
Explanation opens after your attempt
Correct Answer
B. एक अलग / One distinct
Step 1
Concept
(x-2 +4x+4=(x+2)2 ), so there is only one distinct zero. Tip: recognize a perfect square.
Step 2
Why this answer is correct
The correct answer is B. एक अलग / One distinct. (x-2 +4x+4=(x+2)2 ), so there is only one distinct zero. Tip: recognize a perfect square.
Step 3
Exam Tip
(x-2 +4x+4=(x+2)2 ) इसलिए केवल एक अलग शून्यक है। टिप: पूर्ण वर्ग को पहचानें।
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Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
एक द्विघात आलेख (x)-अक्ष को नहीं काटता और उसका शीर्ष (x)-अक्ष के ऊपर है। वास्तविक शून्यकों की संख्या क्या है?
A quadratic graph does not cut the (x)-axis and its vertex is above the (x)-axis. What is the number of real zeroes?
#quadratic vertex no zero
A दो / Two
B एक / One
C शून्य / Zero
D तीन / Three
Explanation opens after your attempt
Correct Answer
C. शून्य / Zero
Step 1
Concept
The graph does not meet the (x)-axis, so there is no real zero. Tip: the vertex position can help judge intersections.
Step 2
Why this answer is correct
The correct answer is C. शून्य / Zero. The graph does not meet the (x)-axis, so there is no real zero. Tip: the vertex position can help judge intersections.
Step 3
Exam Tip
आलेख (x)-अक्ष से नहीं मिलता इसलिए कोई वास्तविक शून्यक नहीं है। टिप: शीर्ष की स्थिति से भी कटान का अंदाजा लग सकता है।
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Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि किसी बहुपद का आलेख ((2,0)) पर स्पर्श करता है और ((5,0)) पर काटता है तो अलग वास्तविक शून्यक कितने हैं?
If a polynomial graph touches at ((2,0)) and crosses at ((5,0)), how many distinct real zeroes are there?
#touching crossing zeroes
A एक / One
B दो / Two
C तीन / Three
D शून्य / Zero
Explanation opens after your attempt
Step 1
Concept
Both touching and crossing show meeting the (x)-axis. Tip: count distinct (x)-values.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. Both touching and crossing show meeting the (x)-axis. Tip: count distinct (x)-values.
Step 3
Exam Tip
स्पर्श और कटान दोनों (x)-अक्ष से मिलना दिखाते हैं। टिप: अलग (x)-मान गिनें।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(x)) का ग्राफ (x)-अक्ष को ((2,0)) पर काटता है और ((-1,0)) पर स्पर्श करता है, तो अलग वास्तविक शून्यक कितने हैं?
If the graph of (p(x)) cuts the (x)-axis at ((2,0)) and touches it at ((-1,0)), how many distinct real zeroes are there?
#distinct zeroes
#touching
#crossing
A एक / One
B दो / Two
C तीन / Three
D शून्य / Zero
Explanation opens after your attempt
Step 1
Concept
Both cutting and touching give zeroes (2) and (-1). Tip: count distinct (x)-values.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. Both cutting and touching give zeroes (2) and (-1). Tip: count distinct (x)-values.
Step 3
Exam Tip
कटान और स्पर्श दोनों से (x)-मान (2) और (-1) शून्यक हैं। टिप: अलग (x)-मानों की गिनती करें।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(x)=-x-2 +25), तो ग्राफ के वास्तविक शून्यक कौन से होंगे?
If (p(x)=-x-2 +25), what will be the real zeroes of the graph?
#quadratic zeroes
#downward parabola
#graph
A (5) और (-5) / (5) and (-5)
B (25) और (-25) / (25) and (-25)
C केवल (0) / Only (0)
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
A. (5) और (-5) / (5) and (-5)
Step 1
Concept
From \(-x^2+25=0\), \(x^2=25\), so \(x=\pm5\). Tip: even with a negative sign, set (y=0).
Step 2
Why this answer is correct
The correct answer is A. (5) और (-5) / (5) and (-5). From \(-x^2+25=0\), \(x^2=25\), so \(x=\pm5\). Tip: even with a negative sign, set (y=0).
Step 3
Exam Tip
\(-x^2+25=0\) से \(x^2=25\), इसलिए \(x=\pm5\) है। टिप: ऋण चिह्न देखकर भी (y=0) रखना न भूलें।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी घन बहुपद का ग्राफ (x)-अक्ष को केवल एक बार काटता है, तो वास्तविक शून्यकों की संख्या क्या मानी जाएगी?
If the graph of a cubic polynomial cuts the (x)-axis only once, what is the number of real zeroes?
#cubic graph
#real zero
#count
A एक / One
B दो / Two
C तीन / Three
D शून्य / Zero
Explanation opens after your attempt
Step 1
Concept
There is only one intersection, so there is one real zero. Tip: a cubic can have at most three real zeroes, not necessarily three.
Step 2
Why this answer is correct
The correct answer is A. एक / One. There is only one intersection, so there is one real zero. Tip: a cubic can have at most three real zeroes, not necessarily three.
Step 3
Exam Tip
कटान केवल एक है इसलिए एक वास्तविक शून्यक है। टिप: घन बहुपद में अधिकतम तीन वास्तविक शून्यक हो सकते हैं, जरूरी नहीं कि तीन हों।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
किस स्थिति में रैखिक बहुपद का कोई वास्तविक शून्यक नहीं होगा?
In which situation will a linear polynomial have no real zero?
#linear graph
#no zero
#constant
A जब उसका ग्राफ (x)-अक्ष को काटे / When its graph cuts the (x)-axis
B जब उसका ग्राफ (x)-अक्ष के समांतर और ऊपर हो / When its graph is parallel to and above the (x)-axis
C जब उसका ग्राफ मूल बिंदु से गुजरे / When its graph passes through the origin
D जब उसका ग्राफ (y)-अक्ष को काटे / When its graph cuts the (y)-axis
Explanation opens after your attempt
Correct Answer
B. जब उसका ग्राफ (x)-अक्ष के समांतर और ऊपर हो / When its graph is parallel to and above the (x)-axis
Step 1
Concept
A line parallel to and above the (x)-axis does not meet the (x)-axis. Tip: such a graph behaves like a non-zero constant polynomial.
Step 2
Why this answer is correct
The correct answer is B. जब उसका ग्राफ (x)-अक्ष के समांतर और ऊपर हो / When its graph is parallel to and above the (x)-axis. A line parallel to and above the (x)-axis does not meet the (x)-axis. Tip: such a graph behaves like a non-zero constant polynomial.
Step 3
Exam Tip
(x)-अक्ष के समांतर ऊपर रेखा (x)-अक्ष से नहीं मिलती। टिप: ऐसा ग्राफ अशून्य स्थिर बहुपद जैसा होता है।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
किस ग्राफ में ठीक एक वास्तविक शून्यक होगा?
Which graph will have exactly one real zero?
#one zero
#graph
#concept
A जो (x)-अक्ष को दो अलग बिंदुओं पर काटे / One that cuts the (x)-axis at two distinct points
B जो (x)-अक्ष को एक ही बिंदु पर स्पर्श करे / One that touches the (x)-axis at only one point
C जो (x)-अक्ष के समांतर ऊपर हो / One that is parallel above the (x)-axis
D जो (y)-अक्ष को दो बार काटे / One that cuts the (y)-axis twice
Explanation opens after your attempt
Correct Answer
B. जो (x)-अक्ष को एक ही बिंदु पर स्पर्श करे / One that touches the (x)-axis at only one point
Step 1
Concept
One touching point gives one real zero. Tip: zeroes depend on meeting the (x)-axis.
Step 2
Why this answer is correct
The correct answer is B. जो (x)-अक्ष को एक ही बिंदु पर स्पर्श करे / One that touches the (x)-axis at only one point. One touching point gives one real zero. Tip: zeroes depend on meeting the (x)-axis.
Step 3
Exam Tip
एक ही स्पर्श बिंदु एक वास्तविक शून्यक देता है। टिप: शून्यक (x)-अक्ष से मिलने पर निर्भर है।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि ग्राफ (x=-2) पर (x)-अक्ष को पार करता है और (x=3) पर केवल छूता है, तो अलग वास्तविक शून्यक कौन से हैं?
If a graph crosses the (x)-axis at (x=-2) and only touches it at (x=3), what are the distinct real zeroes?
#crossing
#touching
#distinct zeroes
A केवल (-2) / Only (-2)
B केवल (3) / Only (3)
C (-2) और (3) / (-2) and (3)
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
C. (-2) और (3) / (-2) and (3)
Step 1
Concept
Both crossing and touching give (p(x)=0). Tip: write both (x)-values as distinct zeroes.
Step 2
Why this answer is correct
The correct answer is C. (-2) और (3) / (-2) and (3). Both crossing and touching give (p(x)=0). Tip: write both (x)-values as distinct zeroes.
Step 3
Exam Tip
पार करना और छूना दोनों (p(x)=0) देते हैं। टिप: अलग शून्यक में दोनों (x)-मान लिखें।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि परवलय (x)-अक्ष को नहीं काटता लेकिन (y)-अक्ष को ((0,-2)) पर काटता है, तो वास्तविक शून्यकों की संख्या क्या है?
If a parabola does not cut the (x)-axis but cuts the (y)-axis at ((0,-2)), what is the number of real zeroes?
#no zero
#y intercept
#parabola
A शून्य / Zero
B एक / One
C दो / Two
D तीन / Three
Explanation opens after your attempt
Correct Answer
A. शून्य / Zero
Step 1
Concept
A (y)-axis intercept does not give a zero because (p(x)\neq0). Tip: meeting the (x)-axis is necessary for a zero.
Step 2
Why this answer is correct
The correct answer is A. शून्य / Zero. A (y)-axis intercept does not give a zero because (p(x)\neq0). Tip: meeting the (x)-axis is necessary for a zero.
Step 3
Exam Tip
(y)-अक्ष कटान शून्यक नहीं देता, क्योंकि (p(x)=0) नहीं है। टिप: शून्यक के लिए (x)-अक्ष से मिलना जरूरी है।
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Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
किसी बहुपद का ग्राफ (x)-अक्ष को दो बार काटता है और (y)-अक्ष को एक बार काटता है। वास्तविक शून्यक कितने हैं?
A polynomial graph cuts the (x)-axis twice and the (y)-axis once. How many real zeroes does it have?
#x axis
#y axis
#zero count
A एक / One
B दो / Two
C तीन / Three
D निर्धारित नहीं / Not determined
Explanation opens after your attempt
Step 1
Concept
Real zeroes are counted only from (x)-axis intersections. Tip: do not add the (y)-axis intercept to zeroes.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. Real zeroes are counted only from (x)-axis intersections. Tip: do not add the (y)-axis intercept to zeroes.
Step 3
Exam Tip
वास्तविक शून्यक केवल (x)-अक्ष कटान से गिने जाते हैं। टिप: (y)-अक्ष कटान को शून्यक में न जोड़ें।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
द्विघात बहुपद का ग्राफ नीचे की ओर खुलता है और (x)-अक्ष को दो बिंदुओं पर काटता है। वास्तविक शून्यकों की संख्या क्या है?
The graph of a quadratic polynomial opens downward and cuts the (x)-axis at two points. What is the number of real zeroes?
#quadratic graph
#real zeroes
#parabola
A शून्य / Zero
B एक / One
C दो / Two
D तीन / Three
Explanation opens after your attempt
Step 1
Concept
The opening direction does not change the count, there are two intersections. Tip: decide zeroes by (x)-axis intersections.
Step 2
Why this answer is correct
The correct answer is C. दो / Two. The opening direction does not change the count, there are two intersections. Tip: decide zeroes by (x)-axis intersections.
Step 3
Exam Tip
दिशा ऊपर या नीचे होने से संख्या नहीं बदलती, कटान दो हैं। टिप: शून्यकों की संख्या (x)-अक्ष कटान से तय करें।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
एक ग्राफ (x)-अक्ष के ऊपर ही रहता है और उसे कहीं नहीं काटता। उस बहुपद के वास्तविक शून्यक कितने हैं?
A graph stays entirely above the (x)-axis and never cuts it. How many real zeroes does that polynomial have?
#no real zero
#graph
#concept
A शून्य / Zero
B एक / One
C दो / Two
D अनंत / Infinite
Explanation opens after your attempt
Correct Answer
A. शून्य / Zero
Step 1
Concept
When the graph does not meet the (x)-axis, (p(x)=0) never occurs. Tip: a real zero is seen on the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. शून्य / Zero. When the graph does not meet the (x)-axis, (p(x)=0) never occurs. Tip: a real zero is seen on the (x)-axis.
Step 3
Exam Tip
जब आलेख (x)-अक्ष से नहीं मिलता तो (p(x)=0) नहीं होता। टिप: वास्तविक शून्यक हमेशा (x)-अक्ष पर दिखता है।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी द्विघात बहुपद का परवलय (x)-अक्ष को केवल ((3,0)) पर स्पर्श करता है, तो अलग वास्तविक शून्यकों की संख्या क्या होगी?
If the parabola of a quadratic polynomial only touches the (x)-axis at ((3,0)), what is the number of distinct real zeroes?
#quadratic
#tangent
#zeroes
A शून्य / Zero
B एक / One
C दो / Two
D तीन / Three
Explanation opens after your attempt
Step 1
Concept
The touching point gives only one distinct zero (3). Tip: count a repeated zero once when distinct zeroes are asked.
Step 2
Why this answer is correct
The correct answer is B. एक / One. The touching point gives only one distinct zero (3). Tip: count a repeated zero once when distinct zeroes are asked.
Step 3
Exam Tip
स्पर्श बिंदु केवल एक अलग शून्यक (3) देता है। टिप: दोहराए हुए शून्यक को अलग शून्यक में एक बार गिनें।
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Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
किसी बहुपद का आलेख (x)-अक्ष को ((-4,0)), ((1,0)) और ((6,0)) पर काटता है। उसके वास्तविक शून्यकों की संख्या कितनी है?
A polynomial graph cuts the (x)-axis at ((-4,0)), ((1,0)) and ((6,0)). How many real zeroes does it have?
#polynomials
#zeroes
#graph
A एक / One
B दो / Two
C तीन / Three
D चार / Four
Explanation opens after your attempt
Correct Answer
C. तीन / Three
Step 1
Concept
There are three distinct (x)-axis intersections, so there are three real zeroes. Tip: count only points with (y=0).
Step 2
Why this answer is correct
The correct answer is C. तीन / Three. There are three distinct (x)-axis intersections, so there are three real zeroes. Tip: count only points with (y=0).
Step 3
Exam Tip
तीन अलग (x)-अक्ष कटान हैं इसलिए तीन वास्तविक शून्यक हैं। टिप: केवल (y=0) वाले बिंदु गिनें।
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Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
परवलय (x)-अक्ष को ((2,0)) और ((2,0)) पर ही छूता है। अलग वास्तविक शून्यकों की संख्या क्या है?
A parabola touches the (x)-axis only at ((2,0)). What is the number of distinct real zeroes?
#repeated zero graph
A एक / One
B दो / Two
C शून्य / Zero
D चार / Four
Explanation opens after your attempt
Step 1
Concept
For a repeated zero the only distinct (x)-value is (2). Tip: do not count the same point twice for distinct zeroes.
Step 2
Why this answer is correct
The correct answer is A. एक / One. For a repeated zero the only distinct (x)-value is (2). Tip: do not count the same point twice for distinct zeroes.
Step 3
Exam Tip
दोहराया शून्यक होने पर अलग (x)-मान केवल (2) है। टिप: अलग शून्यक गिनते समय समान बिंदु दो बार न गिनें।
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Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
किस आलेख से दो वास्तविक शून्यक मिलेंगे?
Which graph will give two real zeroes?
#two real zeroes
A जो (x)-अक्ष को दो अलग बिंदुओं पर काटे / One that cuts the (x)-axis at two distinct points
B जो (y)-अक्ष को दो बार काटे / One that cuts the (y)-axis twice
C जो (x)-अक्ष के समांतर हो / One that is parallel to the (x)-axis
D जो केवल (y)-अक्ष को छुए / One that only touches the (y)-axis
Explanation opens after your attempt
Correct Answer
A. जो (x)-अक्ष को दो अलग बिंदुओं पर काटे / One that cuts the (x)-axis at two distinct points
Step 1
Concept
Two real zeroes need two distinct (x)-axis intersections. Tip: (y)-axis intersections do not count as zeroes.
Step 2
Why this answer is correct
The correct answer is A. जो (x)-अक्ष को दो अलग बिंदुओं पर काटे / One that cuts the (x)-axis at two distinct points. Two real zeroes need two distinct (x)-axis intersections. Tip: (y)-axis intersections do not count as zeroes.
Step 3
Exam Tip
दो वास्तविक शून्यक के लिए दो अलग (x)-अक्ष कटान चाहिए। टिप: (y)-अक्ष कटान शून्यक नहीं गिनाता।
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Question
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
आलेख में (x)-अक्ष पर केवल बिंदु ((8,0)) दिख रहा है। बहुपद के वास्तविक शून्यक की संख्या क्या है?
Only the point ((8,0)) is visible on the (x)-axis in the graph. What is the number of real zeroes of the polynomial?
#count intersections
A एक / One
B आठ / Eight
C शून्य / Zero
D दो / Two
Explanation opens after your attempt
Step 1
Concept
Only one (x)-axis intersection is visible so there is one real zero. Tip: the count comes from the number of points.
Step 2
Why this answer is correct
The correct answer is A. एक / One. Only one (x)-axis intersection is visible so there is one real zero. Tip: the count comes from the number of points.
Step 3
Exam Tip
केवल एक (x)-अक्ष कटान दिख रहा है इसलिए एक वास्तविक शून्यक है। टिप: संख्या बिंदुओं की गिनती से आती है।
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Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
किसी घन बहुपद का आलेख (x)-अक्ष को तीन अलग-अलग बिंदुओं पर काटता है। वास्तविक शून्यकों की संख्या क्या है?
The graph of a cubic polynomial cuts the (x)-axis at three distinct points. What is the number of real zeroes?
#cubic graph zeroes
A तीन / Three
B दो / Two
C एक / One
D शून्य / Zero
Explanation opens after your attempt
Correct Answer
A. तीन / Three
Step 1
Concept
Three intersection points show three real zeroes. Tip: count each distinct (x)-axis intersection.
Step 2
Why this answer is correct
The correct answer is A. तीन / Three. Three intersection points show three real zeroes. Tip: count each distinct (x)-axis intersection.
Step 3
Exam Tip
तीन कटान बिंदु तीन वास्तविक शून्यक बताते हैं। टिप: प्रत्येक अलग (x)-अक्ष कटान को गिनें।
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Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि किसी द्विघात बहुपद के वास्तविक शून्यक (1) और (4) हैं तो उसका आलेख (x)-अक्ष को किन बिंदुओं पर काटेगा?
If a quadratic polynomial has real zeroes (1) and (4) then at which points will its graph cut the (x)-axis?
#zeroes to points
A ((1,0)) और ((4,0)) / ((1,0)) and ((4,0))
B ((0,1)) और ((0,4)) / ((0,1)) and ((0,4))
C ((1,1)) और ((4,4)) / ((1,1)) and ((4,4))
D ((-1,0)) और ((-4,0)) / ((-1,0)) and ((-4,0))
Explanation opens after your attempt
Correct Answer
A. ((1,0)) और ((4,0)) / ((1,0)) and ((4,0))
Step 1
Concept
A zero (a) gives the intersection point ((a,0)). Tip: do not make the zero the (y)-coordinate.
Step 2
Why this answer is correct
The correct answer is A. ((1,0)) और ((4,0)) / ((1,0)) and ((4,0)). A zero (a) gives the intersection point ((a,0)). Tip: do not make the zero the (y)-coordinate.
Step 3
Exam Tip
शून्यक (a) से कटान बिंदु ((a,0)) बनता है। टिप: शून्यक को (y)-निर्देशांक न बनाएं।
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Question
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
एक परवलय ऊपर की ओर खुलता है और उसका शीर्ष ((0,3)) है। यदि वह (x)-अक्ष को नहीं काटता तो वास्तविक शून्यक कितने हैं?
A parabola opens upward and has vertex ((0,3)). If it does not cut the (x)-axis then how many real zeroes are there?
#parabola above axis
A शून्य / Zero
B एक / One
C दो / Two
D तीन / Three
Explanation opens after your attempt
Correct Answer
A. शून्य / Zero
Step 1
Concept
The graph can stay above the (x)-axis so there is no real zero. Tip: if there is no intersection do not write a zero.
Step 2
Why this answer is correct
The correct answer is A. शून्य / Zero. The graph can stay above the (x)-axis so there is no real zero. Tip: if there is no intersection do not write a zero.
Step 3
Exam Tip
आलेख पूरा (x)-अक्ष से ऊपर रह सकता है इसलिए कोई वास्तविक शून्यक नहीं है। टिप: कटान न हो तो शून्यक न लिखें।
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Question
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
एक आलेख (x)-अक्ष को (-3) और (5) पर काटता है। इसके वास्तविक शून्यक कौन से हैं?
A graph cuts the (x)-axis at (-3) and (5). What are its real zeroes?
#two zeroes intercepts
A (-3) और (5) / (-3) and (5)
B (3) और (-5) / (3) and (-5)
C (-3) और (-5) / (-3) and (-5)
D (0) और (5) / (0) and (5)
Explanation opens after your attempt
Correct Answer
A. (-3) और (5) / (-3) and (5)
Step 1
Concept
The (x)-values of the intersection points are the zeroes. Tip: the (y)-value there is (0).
Step 2
Why this answer is correct
The correct answer is A. (-3) और (5) / (-3) and (5). The (x)-values of the intersection points are the zeroes. Tip: the (y)-value there is (0).
Step 3
Exam Tip
कटान बिंदुओं के (x)-मान शून्यक होते हैं। टिप: (y)-मान यहाँ (0) रहता है।
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Question
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि द्विघात बहुपद का आलेख (x)-अक्ष को कहीं नहीं छूता तो उसके वास्तविक शून्यकों की संख्या क्या होगी?
If the graph of a quadratic polynomial does not meet the (x)-axis anywhere then how many real zeroes does it have?
#quadratic no real zero
A शून्य / Zero
B एक / One
C दो / Two
D असीमित / Infinite
Explanation opens after your attempt
Correct Answer
A. शून्य / Zero
Step 1
Concept
There is no (x)-axis intersection so there is no real zero. Tip: count only meetings with the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. शून्य / Zero. There is no (x)-axis intersection so there is no real zero. Tip: count only meetings with the (x)-axis.
Step 3
Exam Tip
कोई (x)-अक्ष कटान नहीं है इसलिए कोई वास्तविक शून्यक नहीं है। टिप: केवल (x)-अक्ष पर मिलने को गिनें।
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Question
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि परवलय (x)-अक्ष को केवल स्पर्श करता है तो बहुपद के कितने वास्तविक शून्यक माने जाते हैं?
If a parabola only touches the (x)-axis then how many real zeroes does the polynomial have?
#quadratic tangent zero
A एक / One
B दो / Two
C शून्य / Zero
D तीन / Three
Explanation opens after your attempt
Step 1
Concept
When it touches the axis there is only one repeated zero. Tip: touching also means meeting the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. एक / One. When it touches the axis there is only one repeated zero. Tip: touching also means meeting the (x)-axis.
Step 3
Exam Tip
स्पर्श करने पर केवल एक समान शून्यक मिलता है। टिप: छूना भी (x)-अक्ष से मिलना है।
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Question
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि द्विघात बहुपद का आलेख (x)-अक्ष को दो अलग-अलग बिंदुओं पर काटता है तो वास्तविक शून्यकों की संख्या क्या होगी?
If the graph of a quadratic polynomial cuts the (x)-axis at two distinct points then what is the number of real zeroes?
#quadratic zeroes graph
A दो / Two
B एक / One
C शून्य / Zero
D चार / Four
Explanation opens after your attempt
Step 1
Concept
Two intersection points show two real zeroes. Tip: a parabola can cut the (x)-axis at most twice.
Step 2
Why this answer is correct
The correct answer is A. दो / Two. Two intersection points show two real zeroes. Tip: a parabola can cut the (x)-axis at most twice.
Step 3
Exam Tip
दो कटान बिंदु दो वास्तविक शून्यक बताते हैं। टिप: परवलय (x)-अक्ष को अधिकतम दो बार काट सकता है।
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Question
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि किसी बहुपद का कोई वास्तविक शून्यक नहीं है, तो उसका ग्राफ (x)-अक्ष के साथ क्या करेगा?
If a polynomial has no real zero, what will its graph do with the (x)-axis?
#no-real-zero
#graph
#x-axis
#concept
A न तो काटेगा न छुएगा / It will neither cut nor touch it
B हमेशा दो बार काटेगा / It will always cut twice
C हमेशा एक बार छुएगा / It will always touch once
D पूरे (x)-अक्ष पर रहेगा / It will lie on the whole (x)-axis
Explanation opens after your attempt
Correct Answer
A. न तो काटेगा न छुएगा / It will neither cut nor touch it
Step 1
Concept
A real zero appears when the graph meets the (x)-axis. With no real zero, the graph will not meet the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. न तो काटेगा न छुएगा / It will neither cut nor touch it. A real zero appears when the graph meets the (x)-axis. With no real zero, the graph will not meet the (x)-axis.
Step 3
Exam Tip
वास्तविक शून्यक (x)-अक्ष से मिलने पर दिखता है। कोई वास्तविक शून्यक न होने पर ग्राफ (x)-अक्ष से नहीं मिलेगा।
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Question
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि किसी बहुपद का ग्राफ (x)-अक्ष को बिल्कुल दो बार छूता या काटता है, तो वास्तविक शून्यकों की संख्या क्या होगी?
If a polynomial graph touches or cuts the (x)-axis exactly two times, how many real zeroes will it have?
#touch-or-cut
#counting-zeroes
#x-axis
#easy
A दो / Two
B एक / One
C तीन / Three
D कोई नहीं / None
Explanation opens after your attempt
Step 1
Concept
Each distinct meeting with the (x)-axis gives one real zero. If it meets twice, it has two real zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो / Two. Each distinct meeting with the (x)-axis gives one real zero. If it meets twice, it has two real zeroes.
Step 3
Exam Tip
(x)-अक्ष से हर अलग मिलन एक वास्तविक शून्यक देता है। दो बार मिलने पर दो वास्तविक शून्यक होंगे।
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Question
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि ग्राफ (x)-अक्ष को ((m,0)) और ((n,0)) पर काटता है, जहाँ \(m\neq n\), तो वास्तविक शून्यकों की संख्या क्या होगी?
If a graph cuts the (x)-axis at ((m,0)) and ((n,0)), where \(m\neq n\), how many real zeroes will it have?
#general-zeroes
#distinct-points
#x-axis
#easy
A दो / Two
B एक / One
C कोई नहीं / None
D अनंत / Infinite
Explanation opens after your attempt
Step 1
Concept
Two distinct intersection points give two distinct real zeroes. Here the zeroes will be (m) and (n).
Step 2
Why this answer is correct
The correct answer is A. दो / Two. Two distinct intersection points give two distinct real zeroes. Here the zeroes will be (m) and (n).
Step 3
Exam Tip
दो अलग कटाव बिंदु दो अलग वास्तविक शून्यक देते हैं। यहाँ शून्यक (m) और (n) होंगे।
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Question
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि बहुपद के ग्राफ में (x)-अक्ष से मिलने वाले बिंदु ((-9,0)), ((-1,0)), और ((3,0)) हैं, तो वास्तविक शून्यक कितने हैं?
If the points where a polynomial graph meets the (x)-axis are ((-9,0)), ((-1,0)), and ((3,0)), how many real zeroes are there?
#counting-zeroes
#x-intercepts
#graph-reading
#easy
A तीन / Three
B दो / Two
C एक / One
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
A. तीन / Three
Step 1
Concept
Three distinct (x)-axis points show three distinct real zeroes. Their (x)-coordinates are the zeroes.
Step 2
Why this answer is correct
The correct answer is A. तीन / Three. Three distinct (x)-axis points show three distinct real zeroes. Their (x)-coordinates are the zeroes.
Step 3
Exam Tip
तीन अलग (x)-अक्ष बिंदु तीन अलग वास्तविक शून्यक बताते हैं। उनके (x)-निर्देशांक ही शून्यक हैं।
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Question
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि ग्राफ (x)-अक्ष को ((2,0)) पर काटता और ((5,0)) पर छूता है, तो अलग वास्तविक शून्यक कितने हैं?
If a graph cuts the (x)-axis at ((2,0)) and touches it at ((5,0)), how many distinct real zeroes are there?
#distinct-real-zeroes
#touching-cutting
#x-axis
#easy
A दो / Two
B एक / One
C तीन / Three
D कोई नहीं / None
Explanation opens after your attempt
Step 1
Concept
Both cutting and touching mean meeting the (x)-axis. There are two distinct points, so there are two distinct real zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो / Two. Both cutting and touching mean meeting the (x)-axis. There are two distinct points, so there are two distinct real zeroes.
Step 3
Exam Tip
कटना और छूना दोनों (x)-अक्ष से मिलना है। दो अलग बिंदु हैं, इसलिए दो अलग वास्तविक शून्यक हैं।
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Question
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि किसी परवलय का एक ही वास्तविक शून्यक है, तो ग्राफ (x)-अक्ष से कैसे मिलेगा?
If a parabola has exactly one real zero, how will its graph meet the (x)-axis?
#one-real-zero
#parabola
#tangent-case
#easy
A एक बिंदु पर छुएगा / It will touch at one point
B दो बिंदुओं पर काटेगा / It will cut at two points
C कहीं नहीं मिलेगा / It will not meet
D चार बिंदुओं पर काटेगा / It will cut at four points
Explanation opens after your attempt
Correct Answer
A. एक बिंदु पर छुएगा / It will touch at one point
Step 1
Concept
One real zero means the graph meets the (x)-axis at only one point. For a parabola, this is usually the touching case.
Step 2
Why this answer is correct
The correct answer is A. एक बिंदु पर छुएगा / It will touch at one point. One real zero means the graph meets the (x)-axis at only one point. For a parabola, this is usually the touching case.
Step 3
Exam Tip
एक वास्तविक शून्यक का अर्थ है ग्राफ (x)-अक्ष से केवल एक बिंदु पर मिलता है। परवलय में यह सामान्यतः छूने की स्थिति होती है।
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