60 results found for "real-zeroes" in Class 10.
Question
Expert Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
किस मान पर \(x^2-6x+k\) के शून्यक वास्तविक और अपरिमेय होंगे?
For which value of (k) will \(x^2-6x+k\) have real and irrational zeroes?
#discriminant
#parameter
#real-zeroes
A (k=5)
B (k=9)
C (k=10)
D (k=13)
Explanation opens after your attempt
Step 1
Concept
Here (D=36-4k). For (k=10), (D=36-40=-4), so this is not correct.
Step 2
Why this answer is correct
The correct answer is C. (k=10). Here (D=36-4k). For (k=10), (D=36-40=-4), so this is not correct.
Step 3
Exam Tip
यहाँ (D=36-4k) है। (k=10) पर (D=-4) नहीं बल्कि (D=36-40=-4), इसलिए यह सही नहीं है।
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Question
Hard Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 27
यदि (p(x)=x-2 -2x+5) है, तो इसके शून्यक वास्तविक न होने का कारण क्या है?
If (p(x)=x-2 -2x+5), what is the reason its zeroes are not real?
#non-real-zeroes
#discriminant
#real-numbers
A (D<0)
B (D=0)
C (D) पूर्ण वर्ग है / (D) is a perfect square
D (D>0) और पूर्ण वर्ग नहीं है / (D>0) and not a perfect square
Explanation opens after your attempt
Step 1
Concept
Here (D=4-20=-16), which is negative. A negative discriminant means there are no real zeroes.
Step 2
Why this answer is correct
The correct answer is A. (D<0). Here (D=4-20=-16), which is negative. A negative discriminant means there are no real zeroes.
Step 3
Exam Tip
यहाँ (D=4-20=-16), जो ऋणात्मक है। ऋणात्मक विविक्तकर का अर्थ वास्तविक शून्यक नहीं होते।
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Question
Hard Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 27
यदि (p(x)=x-2 -14x+45) और (q(x)=x-2 -14x+43), तो कौन सा कथन सही है?
If (p(x)=x-2 -14x+45) and (q(x)=x-2 -14x+43), which statement is correct?
#discriminant-comparison
#pyq-style
#real-zeroes
A (p(x)) के शून्यक परिमेय हैं और (q(x)) के अपरिमेय वास्तविक हैं / Zeroes of (p(x)) are rational and zeroes of (q(x)) are irrational real
B दोनों के शून्यक परिमेय हैं / Both have rational zeroes
C दोनों के शून्यक अवास्तविक हैं / Both have non-real zeroes
D (p(x)) के अपरिमेय और (q(x)) के परिमेय शून्यक हैं / (p(x)) has irrational and (q(x)) has rational zeroes
Explanation opens after your attempt
Correct Answer
A. (p(x)) के शून्यक परिमेय हैं और (q(x)) के अपरिमेय वास्तविक हैं / Zeroes of (p(x)) are rational and zeroes of (q(x)) are irrational real
Step 1
Concept
For (p(x)), (D=16) is a perfect square, and for (q(x)), (D=24) is positive but not a perfect square. Thus the first has rational and the second irrational real zeroes.
Step 2
Why this answer is correct
The correct answer is A. (p(x)) के शून्यक परिमेय हैं और (q(x)) के अपरिमेय वास्तविक हैं / Zeroes of (p(x)) are rational and zeroes of (q(x)) are irrational real. For (p(x)), (D=16) is a perfect square, and for (q(x)), (D=24) is positive but not a perfect square. Thus the first has rational and the second irrational real zeroes.
Step 3
Exam Tip
(p(x)) के लिए (D=16) पूर्ण वर्ग है और (q(x)) के लिए (D=24) धनात्मक अपूर्ण वर्ग है। इसलिए पहला परिमेय और दूसरा अपरिमेय वास्तविक है।
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Question
Hard Mathematics
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
Polynomials Irrational numbers and real numbers Class 10 Level 28
यदि (p(x)=x-2 -2x-3) है, तो क्या इसके सभी शून्यक वास्तविक हैं?
If (p(x)=x-2 -2x-3), are all its zeroes real?
#real-zeroes
#discriminant
#quadratic
A हाँ, क्योंकि (D=16) / Yes, because (D=16)
B हाँ, क्योंकि (D=8) / Yes, because (D=8)
C नहीं, क्योंकि (D<0) / No, because (D<0)
D नहीं, क्योंकि शून्यक अपरिमेय हैं / No, because the zeroes are irrational
Explanation opens after your attempt
Correct Answer
A. हाँ, क्योंकि (D=16) / Yes, because (D=16)
Step 1
Concept
Here (D=(-2)2 -4(1)(-3)=16), which is positive. So both zeroes are real.
Step 2
Why this answer is correct
The correct answer is A. हाँ, क्योंकि (D=16) / Yes, because (D=16). Here (D=(-2)2 -4(1)(-3)=16), which is positive. So both zeroes are real.
Step 3
Exam Tip
यहाँ (D=(-2)2 -4(1)(-3)=16) है, जो धनात्मक है। इसलिए दोनों शून्यक वास्तविक हैं।
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Question
Hard Mathematics
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Medium Mathematics
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
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
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
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
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
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
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
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
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
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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Question
Medium Mathematics
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
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
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
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
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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Question
Easy Mathematics
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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Question
Easy Mathematics
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
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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Question
Easy Mathematics
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
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
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
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
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
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
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि किसी परवलय के दो वास्तविक शून्यक हैं, तो वह (x)-अक्ष से कैसे मिलेगा?
If a parabola has two real zeroes, how will it meet the (x)-axis?
#quadratic
#two-real-zeroes
#parabola
#graph
A दो अलग-अलग बिंदुओं पर काटेगा / It will cut at two distinct points
B कहीं नहीं मिलेगा / It will not meet anywhere
C एक ही बिंदु पर छुएगा / It will touch at one point
D पूरे (x)-अक्ष पर होगा / It will lie on the whole (x)-axis
Explanation opens after your attempt
Correct Answer
A. दो अलग-अलग बिंदुओं पर काटेगा / It will cut at two distinct points
Step 1
Concept
Two real zeroes show two distinct (x)-axis intersections. Hence the parabola cuts the (x)-axis at two points.
Step 2
Why this answer is correct
The correct answer is A. दो अलग-अलग बिंदुओं पर काटेगा / It will cut at two distinct points. Two real zeroes show two distinct (x)-axis intersections. Hence the parabola cuts the (x)-axis at two points.
Step 3
Exam Tip
दो वास्तविक शून्यक दो अलग (x)-अक्ष कटाव बताते हैं। इसलिए परवलय (x)-अक्ष को दो बिंदुओं पर काटेगा।
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Question
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि ग्राफ (x)-अक्ष के नीचे पूरा बना है और (x)-अक्ष को नहीं छूता, तो वास्तविक शून्यक कितने हैं?
If a graph lies completely below the (x)-axis and does not touch it, how many real zeroes does it have?
#no-real-zero
#below-x-axis
#graph
#easy
A (0)
B (1)
C (2)
D अनंत / Infinite
Explanation opens after your attempt
Step 1
Concept
For a real zero, the graph must meet the (x)-axis. If it stays below and does not touch it, there is no real zero.
Step 2
Why this answer is correct
The correct answer is A. (0). For a real zero, the graph must meet the (x)-axis. If it stays below and does not touch it, there is no real zero.
Step 3
Exam Tip
वास्तविक शून्यक के लिए ग्राफ का (x)-अक्ष से मिलना जरूरी है। नीचे रहने और न छूने पर कोई वास्तविक शून्यक नहीं होगा।
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Question
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि परवलय (x)-अक्ष को ((3,0)) पर केवल छूता है, तो द्विघात बहुपद के वास्तविक शून्यकों की संख्या क्या है?
If a parabola only touches the (x)-axis at ((3,0)), how many real zeroes does the quadratic polynomial have?
#touching-x-axis
#one-zero
#parabola
#easy
A एक / One
B दो / Two
C कोई नहीं / None
D चार / Four
Explanation opens after your attempt
Step 1
Concept
Touching also means meeting the (x)-axis, but there is only one point. Hence there is one real zero.
Step 2
Why this answer is correct
The correct answer is A. एक / One. Touching also means meeting the (x)-axis, but there is only one point. Hence there is one real zero.
Step 3
Exam Tip
छूना भी (x)-अक्ष से मिलना है, लेकिन बिंदु केवल एक है। इसलिए एक वास्तविक शून्यक होगा।
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Question
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि किसी परवलय का (x)-अक्ष से कोई साझा बिंदु नहीं है, तो द्विघात बहुपद के वास्तविक शून्यक कितने होंगे?
If a parabola has no common point with the (x)-axis, how many real zeroes does the quadratic polynomial have?
#quadratic-polynomial
#parabola
#no-real-zero
#graph
A (0)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
Real zeroes are found only when the graph meets the (x)-axis. With no common point, there are (0) real zeroes.
Step 2
Why this answer is correct
The correct answer is A. (0). Real zeroes are found only when the graph meets the (x)-axis. With no common point, there are (0) real zeroes.
Step 3
Exam Tip
वास्तविक शून्यक तभी मिलते हैं जब ग्राफ (x)-अक्ष से मिले। साझा बिंदु न होने पर वास्तविक शून्यक (0) होंगे।
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Question
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि ग्राफ (x)-अक्ष को तीन अलग-अलग बिंदुओं पर काटता है, तो वास्तविक शून्यकों की संख्या क्या होगी?
If a graph cuts the (x)-axis at three distinct points, how many real zeroes will it have?
#real-zeroes
#x-axis
#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
Each distinct intersection with the (x)-axis gives one real zero. Therefore three distinct intersections give three real zeroes.
Step 2
Why this answer is correct
The correct answer is A. तीन / Three. Each distinct intersection with the (x)-axis gives one real zero. Therefore three distinct intersections give three real zeroes.
Step 3
Exam Tip
हर अलग (x)-अक्ष कटाव एक वास्तविक शून्यक देता है। इसलिए तीन अलग कटावों से तीन वास्तविक शून्यक मिलेंगे।
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Question
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
किस स्थिति में द्विघात बहुपद के दो वास्तविक शून्यक होंगे?
In which case will a quadratic polynomial have two real zeroes?
#quadratic-zeroes
#parabola
#x-axis
#concept
A जब उसका ग्राफ (x)-अक्ष को दो अलग बिंदुओं पर काटे / When its graph cuts the (x)-axis at two distinct points
B जब उसका ग्राफ (y)-अक्ष को एक बार काटे / When its graph cuts the (y)-axis once
C जब उसका ग्राफ (x)-अक्ष को न काटे / When its graph does not cut the (x)-axis
D जब उसका ग्राफ केवल ऊपर हो / When its graph is only above
Explanation opens after your attempt
Correct Answer
A. जब उसका ग्राफ (x)-अक्ष को दो अलग बिंदुओं पर काटे / When its graph cuts the (x)-axis at two distinct points
Step 1
Concept
Real zeroes of a quadratic polynomial are found from points where it meets the (x)-axis. Two distinct intersections give two real zeroes.
Step 2
Why this answer is correct
The correct answer is A. जब उसका ग्राफ (x)-अक्ष को दो अलग बिंदुओं पर काटे / When its graph cuts the (x)-axis at two distinct points. Real zeroes of a quadratic polynomial are found from points where it meets the (x)-axis. Two distinct intersections give two real zeroes.
Step 3
Exam Tip
द्विघात बहुपद के वास्तविक शून्यक (x)-अक्ष से मिलने वाले बिंदुओं से मिलते हैं। दो अलग कटाव दो वास्तविक शून्यक देते हैं।
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Question
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि परवलय (x)-अक्ष को ((-1,0)) और ((5,0)) पर काटता है, तो वास्तविक शून्यकों की संख्या क्या है?
If a parabola cuts the (x)-axis at ((-1,0)) and ((5,0)), how many real zeroes are there?
#parabola
#two-zeroes
#x-intercepts
#easy
A दो / Two
B एक / One
C कोई नहीं / None
D तीन / Three
Explanation opens after your attempt
Step 1
Concept
Two distinct (x)-axis intersections show two real zeroes. Here the zeroes are (-1) and (5).
Step 2
Why this answer is correct
The correct answer is A. दो / Two. Two distinct (x)-axis intersections show two real zeroes. Here the zeroes are (-1) and (5).
Step 3
Exam Tip
दो अलग-अलग (x)-अक्ष कटाव दो वास्तविक शून्यक बताते हैं। यहाँ शून्यक (-1) और (5) हैं।
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Question
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी बहुपद के ग्राफ के (x)-अक्ष से दो कटाव हैं, तो उसके वास्तविक शून्यकों की संख्या क्या होगी?
If a polynomial graph has two intersections with the (x)-axis, how many real zeroes does it have?
#real-zeroes
#x-axis-intersections
#polynomial-graph
#easy
A दो / Two
B एक / One
C कोई नहीं / None
D चार / Four
Explanation opens after your attempt
Step 1
Concept
Each distinct intersection with the (x)-axis gives one real zero. With two intersections, there are two real zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो / Two. Each distinct intersection with the (x)-axis gives one real zero. With two intersections, there are two real zeroes.
Step 3
Exam Tip
(x)-अक्ष से प्रत्येक अलग कटाव एक वास्तविक शून्यक देता है। दो कटाव होने पर दो वास्तविक शून्यक होंगे।
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Question
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि परवलय पूरा (x)-अक्ष के ऊपर है, तो द्विघात बहुपद के कितने वास्तविक शून्यक होंगे?
If a parabola lies completely above the (x)-axis, how many real zeroes does the quadratic polynomial have?
#quadratic-graph
#no-real-zero
#parabola
#easy
A कोई नहीं / None
B एक / One
C दो / Two
D अनंत / Infinite
Explanation opens after your attempt
Correct Answer
A. कोई नहीं / None
Step 1
Concept
If the graph does not meet the (x)-axis, no real value satisfies (p(x)=0). Therefore it has (0) real zeroes.
Step 2
Why this answer is correct
The correct answer is A. कोई नहीं / None. If the graph does not meet the (x)-axis, no real value satisfies (p(x)=0). Therefore it has (0) real zeroes.
Step 3
Exam Tip
यदि ग्राफ (x)-अक्ष से नहीं मिलता, तो (p(x)=0) का कोई वास्तविक मान नहीं मिलता। इसलिए वास्तविक शून्यक (0) होंगे।
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Question
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि परवलय (x)-अक्ष को केवल छूता है, काटता नहीं है, तो द्विघात बहुपद के वास्तविक शून्यकों की संख्या क्या होगी?
If a parabola only touches the (x)-axis and does not cut it, how many real zeroes does the quadratic polynomial have?
#parabola
#touching-x-axis
#one-zero
#quadratic
A एक / One
B दो / Two
C कोई नहीं / None
D तीन / Three
Explanation opens after your attempt
Step 1
Concept
When a parabola touches the (x)-axis at one point, it has one real zero. In exams, touching the (x)-axis also counts as meeting it.
Step 2
Why this answer is correct
The correct answer is A. एक / One. When a parabola touches the (x)-axis at one point, it has one real zero. In exams, touching the (x)-axis also counts as meeting it.
Step 3
Exam Tip
जब परवलय (x)-अक्ष को केवल एक बिंदु पर छूता है, तो एक वास्तविक शून्यक होता है। परीक्षा में छूना भी (x)-अक्ष से मिलना माना जाता है।
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Question
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी बहुपद का ग्राफ (x)-अक्ष को नहीं काटता और नहीं छूता, तो उसके वास्तविक शून्यकों की संख्या क्या होगी?
If the graph of a polynomial neither cuts nor touches the (x)-axis, how many real zeroes does it have?
#real-zeroes
#no-intersection
#polynomial-graph
#easy
A (0)
B (1)
C (2)
D अनंत / Infinite
Explanation opens after your attempt
Step 1
Concept
Real zeroes appear only where the graph meets the (x)-axis. If it does not meet the (x)-axis, it has no real zero.
Step 2
Why this answer is correct
The correct answer is A. (0). Real zeroes appear only where the graph meets the (x)-axis. If it does not meet the (x)-axis, it has no real zero.
Step 3
Exam Tip
वास्तविक शून्यक तभी दिखते हैं जब ग्राफ (x)-अक्ष से मिले। यदि ग्राफ (x)-अक्ष से नहीं मिलता, तो वास्तविक शून्यक नहीं होंगे।
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