Question 1/180
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि किसी ग्राफ में (x)-अक्ष से प्रतिच्छेद (\(-\sqrt{3},0\)) है तो शून्यक क्या है?
If a graph has (x)-axis intersection (\(-\sqrt{3},0\)), what is the zero?
#irrational-zero
#x-intercept
#graph
A \(-\sqrt{3}\)
B \(\sqrt{3}\)
C (0)
D (\(-\sqrt{3},0\))
Explanation opens after your attempt
Correct Answer
A. \(-\sqrt{3}\)
Step 1
Concept
A zero is the (x)-coordinate of the intercept. An irrational number can also be a zero.
Step 2
Why this answer is correct
The correct answer is A. \(-\sqrt{3}\). A zero is the (x)-coordinate of the intercept. An irrational number can also be a zero.
Step 3
Exam Tip
शून्यक प्रतिच्छेद का (x)-निर्देशांक होता है। अपरिमेय संख्या भी शून्यक हो सकती है।
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Question 2/180
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
किसी बहुपद का ग्राफ (x)-अक्ष को केवल सम संख्याओं (-4), (2), और (8) पर काटता है। शून्यकों की संख्या क्या है?
A polynomial graph cuts the (x)-axis only at the even numbers (-4), (2), and (8). What is the number of zeroes?
#counting-zeroes
#graph
#integer-zeroes
A तीन / Three
B दो / Two
C छह / Six
D एक / One
Explanation opens after your attempt
Correct Answer
A. तीन / Three
Step 1
Concept
Three distinct (x)-intercepts give three zeroes. Count by intersections not by the type of numbers.
Step 2
Why this answer is correct
The correct answer is A. तीन / Three. Three distinct (x)-intercepts give three zeroes. Count by intersections not by the type of numbers.
Step 3
Exam Tip
तीन अलग (x)-प्रतिच्छेद तीन शून्यक देते हैं। संख्या के प्रकार से नहीं बल्कि प्रतिच्छेदों से गिनें।
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Question 3/180
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि ग्राफ (x)-अक्ष को (2.5) पर काटता है तो सही शून्यक कौन सा है?
If a graph cuts the (x)-axis at (2.5), which is the correct zero?
#zero-vs-point
#decimal
#graph
A (2.5)
B ((2.5,0))
C (0)
D ((0,2.5))
Explanation opens after your attempt
Step 1
Concept
A zero is a number not a point. The point is ((2.5,0)) but the zero is (2.5).
Step 2
Why this answer is correct
The correct answer is A. (2.5). A zero is a number not a point. The point is ((2.5,0)) but the zero is (2.5).
Step 3
Exam Tip
शून्यक संख्या होता है बिंदु नहीं। बिंदु ((2.5,0)) है लेकिन शून्यक (2.5) है।
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Question 4/180
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
शून्य बहुपद (p(x)=0) के ग्राफ के बारे में कौन सा कथन सही है?
Which statement is correct about the graph of the zero polynomial (p(x)=0)?
#zero-polynomial
#graph
#conceptual
A पूरा ग्राफ (x)-अक्ष है / The whole graph is the (x)-axis
B ग्राफ (y)-अक्ष है / The graph is the (y)-axis
C कोई बिंदु नहीं है / There is no point
D केवल ((0,0)) है / It is only ((0,0))
Explanation opens after your attempt
Correct Answer
A. पूरा ग्राफ (x)-अक्ष है / The whole graph is the (x)-axis
Step 1
Concept
(p(x)=0) gives (y=0) for every (x). Therefore the whole (x)-axis is the graph.
Step 2
Why this answer is correct
The correct answer is A. पूरा ग्राफ (x)-अक्ष है / The whole graph is the (x)-axis. (p(x)=0) gives (y=0) for every (x). Therefore the whole (x)-axis is the graph.
Step 3
Exam Tip
(p(x)=0) हर (x) के लिए (y=0) देता है। इसलिए पूरा (x)-अक्ष ग्राफ है।
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Question 5/180
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 6/180
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 7/180
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 8/180
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
एक ग्राफ (x)-अक्ष को तीन बार काटता है। उस बहुपद की न्यूनतम संभावित डिग्री क्या हो सकती है?
A graph cuts the (x)-axis three times. What can be the minimum possible degree of that polynomial?
#degree
#maximum-zeroes
#graph
A (3)
B (2)
C (1)
D (0)
Explanation opens after your attempt
Step 1
Concept
The number of real zeroes cannot exceed the degree of the polynomial. Three crossings need minimum degree (3).
Step 2
Why this answer is correct
The correct answer is A. (3). The number of real zeroes cannot exceed the degree of the polynomial. Three crossings need minimum degree (3).
Step 3
Exam Tip
किसी बहुपद के वास्तविक शून्यकों की संख्या उसकी डिग्री से अधिक नहीं हो सकती। तीन कटान के लिए न्यूनतम डिग्री (3) है।
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Question 9/180
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि किसी बहुपद के ग्राफ के (x)-प्रतिच्छेद ((-4,0)), ((1,0)), और ((6,0)) हैं तो शून्यकों का समुच्चय क्या है?
If the (x)-intercepts of a polynomial graph are ((-4,0)), ((1,0)), and ((6,0)), what is the set of zeroes?
#x-intercepts
#set-of-zeroes
#graph
A ({-4,1,6})
B ({0,1,6})
C ({-4,0,6})
D ({-4,1,0})
Explanation opens after your attempt
Correct Answer
A. ({-4,1,6})
Step 1
Concept
A zero is the (x)-coordinate of the intercept point. Do not write (y=0) as the zero.
Step 2
Why this answer is correct
The correct answer is A. ({-4,1,6}). A zero is the (x)-coordinate of the intercept point. Do not write (y=0) as the zero.
Step 3
Exam Tip
शून्यक प्रतिच्छेद बिंदु का (x)-निर्देशांक होता है। (y=0) को शून्यक न लिखें।
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Question 10/180
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 11/180
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
एक द्विघात बहुपद का ग्राफ (x)-अक्ष को एक ही बिंदु ((4,0)) पर छूता है। उसके शून्यक कैसे होंगे?
The graph of a quadratic polynomial touches the (x)-axis at only one point ((4,0)). What type of zeroes does it have?
#quadratic
#equal-zeroes
#graph
A बराबर शून्यक (4) और (4) / Equal zeroes (4) and (4)
B भिन्न शून्यक (4) और (0) / Distinct zeroes (4) and (0)
C कोई शून्यक नहीं / No zero
D तीन शून्यक / Three zeroes
Explanation opens after your attempt
Correct Answer
A. बराबर शून्यक (4) और (4) / Equal zeroes (4) and (4)
Step 1
Concept
When a quadratic graph touches at one point its two zeroes are equal. Treat it as a repeated zero in exams.
Step 2
Why this answer is correct
The correct answer is A. बराबर शून्यक (4) और (4) / Equal zeroes (4) and (4). When a quadratic graph touches at one point its two zeroes are equal. Treat it as a repeated zero in exams.
Step 3
Exam Tip
द्विघात ग्राफ एक बिंदु पर छूता है तो दोनों शून्यक समान होते हैं। परीक्षा में इसे दोहराया शून्यक मानें।
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Question 12/180
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि किसी रैखिक बहुपद का ग्राफ (x)-अक्ष के समानांतर है और (x)-अक्ष पर नहीं है तो उसके शून्यक कितने होंगे?
If the graph of a linear polynomial is parallel to the (x)-axis and not on the (x)-axis, how many zeroes will it have?
#linear-polynomial
#no-zero
#graph
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
Such a line never meets the (x)-axis so it has no zero. First check the intercept from the graph.
Step 2
Why this answer is correct
The correct answer is A. शून्य / Zero. Such a line never meets the (x)-axis so it has no zero. First check the intercept from the graph.
Step 3
Exam Tip
ऐसी रेखा कभी (x)-अक्ष से नहीं मिलती इसलिए कोई शून्यक नहीं होता। ग्राफ से पहले प्रतिच्छेद देखें।
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Question 13/180
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि किसी ग्राफ के (x)-अक्ष कटान ((-4,0)), ((6,0)), ((16,0)) हैं, तो इनके शून्यकों का माध्य क्या है?
If the (x)-axis intersections of a graph are ((-4,0)), ((6,0)), ((16,0)), what is the mean of their zeroes?
#mean of zeroes
#graph
#intercepts
A (6)
B (18)
C (-6)
D (16)
Explanation opens after your attempt
Step 1
Concept
The mean is \(\frac{-4+6+16}{3}=6\). Tip: first read the (x)-values from intersection points.
Step 2
Why this answer is correct
The correct answer is A. (6). The mean is \(\frac{-4+6+16}{3}=6\). Tip: first read the (x)-values from intersection points.
Step 3
Exam Tip
माध्य \(\frac{-4+6+16}{3}=6\) है। टिप: पहले कटान बिंदुओं से (x)-मान पढ़ें।
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Question 14/180
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=x-2 +gx+g-2 ) और \(g\neq0\) है, तो ग्राफ (x)-अक्ष को क्यों नहीं काटेगा?
If (p(x)=x-2 +gx+g-2 ) and \(g\neq0\), why will the graph not cut the (x)-axis?
#discriminant
#no real zero
#graph
A क्योंकि इसका विविक्तकर ऋणात्मक है / Because its discriminant is negative
B क्योंकि यह रैखिक है / Because it is linear
C क्योंकि (0) शून्यक है / Because (0) is a zero
D क्योंकि हर (x) शून्यक है / Because every (x) is a zero
Explanation opens after your attempt
Correct Answer
A. क्योंकि इसका विविक्तकर ऋणात्मक है / Because its discriminant is negative
Step 1
Concept
The discriminant is \(g^2-4g^2=-3g^2<0\), so there are no real zeroes. Tip: a negative discriminant means no (x)-axis intersection.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि इसका विविक्तकर ऋणात्मक है / Because its discriminant is negative. The discriminant is \(g^2-4g^2=-3g^2<0\), so there are no real zeroes. Tip: a negative discriminant means no (x)-axis intersection.
Step 3
Exam Tip
विविक्तकर \(g^2-4g^2=-3g^2<0\) है, इसलिए वास्तविक शून्यक नहीं हैं। टिप: ऋणात्मक विविक्तकर का अर्थ (x)-अक्ष कटान नहीं है।
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Question 15/180
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(-12)=0), (p(-2)=6), (p(4)=0), (p(15)=0) है, तो कितने दिए गए (x)-मान शून्यक हैं?
If (p(-12)=0), (p(-2)=6), (p(4)=0), (p(15)=0), how many of the given (x)-values are zeroes?
#function table
#count zeroes
#graph
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 function value is (0) at (-12), (4), and (15). Tip: do not treat (p(-2)=6) as a zero.
Step 2
Why this answer is correct
The correct answer is B. तीन / Three. The function value is (0) at (-12), (4), and (15). Tip: do not treat (p(-2)=6) as a zero.
Step 3
Exam Tip
(-12), (4), (15) पर फलन मान (0) है। टिप: (p(-2)=6) को शून्यक न मानें।
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Question 16/180
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 17/180
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि नीचे खुलने वाले परवलय के शून्यक (-5) और (13) हैं, तो (x=2) पर ग्राफ कहाँ होगा?
If a downward-opening parabola has zeroes (-5) and (13), where will the graph be at (x=2)?
#downward parabola
#sign inside zeroes
#graph
A (x)-अक्ष के ऊपर / Above the (x)-axis
B (x)-अक्ष के नीचे / Below the (x)-axis
C ठीक (x)-अक्ष पर / Exactly on the (x)-axis
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. (x)-अक्ष के ऊपर / Above the (x)-axis
Step 1
Concept
For a downward-opening parabola, values between the two zeroes are positive. Tip: (x=2) lies between the zeroes.
Step 2
Why this answer is correct
The correct answer is A. (x)-अक्ष के ऊपर / Above the (x)-axis. For a downward-opening parabola, values between the two zeroes are positive. Tip: (x=2) lies between the zeroes.
Step 3
Exam Tip
नीचे खुलने वाले परवलय में दो शून्यकों के बीच मान धनात्मक होते हैं। टिप: (x=2) दोनों शून्यकों के बीच है।
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Question 18/180
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=x-2 -19x+90) है, तो ग्राफ के शून्यकों के बीच दूरी कितनी है?
If (p(x)=x-2 -19x+90), what is the distance between the zeroes of the graph?
#distance between zeroes
#quadratic
#graph
A (1)
B (9)
C (19)
D (90)
Explanation opens after your attempt
Step 1
Concept
(x-2 -19x+90=(x-9)(x-10)), so the distance is (10-9=1). Tip: find zeroes first and then take distance.
Step 2
Why this answer is correct
The correct answer is A. (1). (x-2 -19x+90=(x-9)(x-10)), so the distance is (10-9=1). Tip: find zeroes first and then take distance.
Step 3
Exam Tip
(x-2 -19x+90=(x-9)(x-10)) है, इसलिए दूरी (10-9=1) है। टिप: पहले शून्यक निकालें फिर दूरी लें।
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Question 19/180
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=-(x-11)(x+13)) है, तो (x<-13) के लिए ग्राफ (x)-अक्ष के किस ओर होगा?
If (p(x)=-(x-11)(x+13)), on which side of the (x)-axis will the graph lie for (x<-13)?
#sign region
#factor form
#graph
A ऊपर / Above
B नीचे / Below
C (x)-अक्ष पर / On the (x)-axis
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
B. नीचे / Below
Step 1
Concept
For (x<-13), both factors are negative and the outside negative makes the value negative. Tip: check factor signs first.
Step 2
Why this answer is correct
The correct answer is B. नीचे / Below. For (x<-13), both factors are negative and the outside negative makes the value negative. Tip: check factor signs first.
Step 3
Exam Tip
(x<-13) पर दोनों कारक ऋणात्मक हैं और बाहर का ऋण चिन्ह मान को ऋणात्मक बनाता है। टिप: पहले कारकों का चिह्न देखें।
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Question 20/180
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=6x-2 -72x+216) है, तो ग्राफ (x)-अक्ष से कैसे मिलेगा?
If (p(x)=6x-2 -72x+216), how will the graph meet the (x)-axis?
#complete square
#tangent
#graph
A (x=6) पर स्पर्श करेगा / It will touch at (x=6)
B (x=-6) पर स्पर्श करेगा / It will touch at (x=-6)
C दो अलग बिंदुओं पर काटेगा / It will cut at two distinct points
D कहीं नहीं मिलेगा / It will not meet
Explanation opens after your attempt
Correct Answer
A. (x=6) पर स्पर्श करेगा / It will touch at (x=6)
Step 1
Concept
(6x-2 -72x+216=6(x-6)2 ), so it touches at (x=6). Tip: the outside (6) does not change the zero.
Step 2
Why this answer is correct
The correct answer is A. (x=6) पर स्पर्श करेगा / It will touch at (x=6). (6x-2 -72x+216=6(x-6)2 ), so it touches at (x=6). Tip: the outside (6) does not change the zero.
Step 3
Exam Tip
(6x-2 -72x+216=6(x-6)2 ) है, इसलिए (x=6) पर स्पर्श होगा। टिप: बाहरी (6) शून्यक नहीं बदलता।
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Question 21/180
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=x-3 -12x-2 +35x) है, तो ग्राफ के शून्यकों का समूह कौन सा है?
If (p(x)=x-3 -12x-2 +35x), what is the set of zeroes of the graph?
#cubic factorization
#zeroes
#graph
A (0,5,7)
B (0,-5,-7)
C (5,7,12)
D केवल (0) / Only (0)
Explanation opens after your attempt
Correct Answer
A. (0,5,7)
Step 1
Concept
(x-3 -12x-2 +35x=x(x-5)(x-7)), so the zeroes are (0), (5), (7). Tip: first take (x) as the common factor.
Step 2
Why this answer is correct
The correct answer is A. (0,5,7). (x-3 -12x-2 +35x=x(x-5)(x-7)), so the zeroes are (0), (5), (7). Tip: first take (x) as the common factor.
Step 3
Exam Tip
(x-3 -12x-2 +35x=x(x-5)(x-7)) है, इसलिए शून्यक (0), (5), (7) हैं। टिप: पहले (x) सामान्य गुणनखंड निकालें।
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Question 22/180
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि कोई बहुपद (x)-अक्ष को आठ अलग बिंदुओं पर काटता है, तो न्यूनतम संभावित घात क्या होगी?
If a polynomial cuts the (x)-axis at eight distinct points, what is the minimum possible degree?
#minimum degree
#distinct zeroes
#graph
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
For eight distinct real zeroes, the degree must be at least (8). Tip: the number of distinct zeroes cannot exceed the degree.
Step 2
Why this answer is correct
The correct answer is C. (8). For eight distinct real zeroes, the degree must be at least (8). Tip: the number of distinct zeroes cannot exceed the degree.
Step 3
Exam Tip
आठ अलग वास्तविक शून्यकों के लिए घात कम से कम (8) होनी चाहिए। टिप: अलग शून्यकों की संख्या घात से अधिक नहीं हो सकती।
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Question 23/180
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=x-4 -1296) है, तो वास्तविक (x)-अक्ष कटान कौन से हैं?
If (p(x)=x-4 -1296), what are the real (x)-axis intersections?
#quartic
#real zeroes
#graph
A ((-6,0)) और ((6,0)) / ((-6,0)) and ((6,0))
B ((-36,0)) और ((36,0)) / ((-36,0)) and ((36,0))
C ((0,0)), ((-6,0)), ((6,0))
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
A. ((-6,0)) और ((6,0)) / ((-6,0)) and ((6,0))
Step 1
Concept
(x-4 -1296=\(x^2-36\)\(x^2+36\)), and the real zeroes are only \(\pm6\). Tip: \(x^2+36\) gives no real zero.
Step 2
Why this answer is correct
The correct answer is A. ((-6,0)) और ((6,0)) / ((-6,0)) and ((6,0)). (x-4 -1296=\(x^2-36\)\(x^2+36\)), and the real zeroes are only \(\pm6\). Tip: \(x^2+36\) gives no real zero.
Step 3
Exam Tip
(x-4 -1296=\(x^2-36\)\(x^2+36\)) है और वास्तविक शून्यक केवल \(\pm6\) हैं। टिप: \(x^2+36\) वास्तविक शून्यक नहीं देता।
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Question 24/180
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=x-2 +px+q) का ग्राफ ((-8,0)) और ((5,0)) पर (x)-अक्ष को काटता है, तो (p) और (q) क्या होंगे?
If the graph of (p(x)=x-2 +px+q) cuts the (x)-axis at ((-8,0)) and ((5,0)), what will (p) and (q) be?
#zeroes to coefficients
#quadratic
#graph
A (p=3, q=-40)
B (p=-3, q=-40)
C (p=13, q=40)
D (p=-13, q=-40)
Explanation opens after your attempt
Correct Answer
A. (p=3, q=-40)
Step 1
Concept
The zeroes are (-8) and (5), so the polynomial is ((x+8)(x-5)=x-2 +3x-40). Tip: form factors from intersections.
Step 2
Why this answer is correct
The correct answer is A. (p=3, q=-40). The zeroes are (-8) and (5), so the polynomial is ((x+8)(x-5)=x-2 +3x-40). Tip: form factors from intersections.
Step 3
Exam Tip
शून्यक (-8) और (5) हैं, इसलिए बहुपद ((x+8)(x-5)=x-2 +3x-40) है। टिप: कटान से गुणनखंड बनाएं।
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Question 25/180
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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Question 26/180
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=36x-2 -49) है, तो ग्राफ के (x)-अक्ष कटान कौन से हैं?
If (p(x)=36x-2 -49), what are the (x)-axis intersections of the graph?
#difference of squares
#fraction zeroes
#graph
A (\left\(\frac{7}{6},0\right\)) और (\left\(-\frac{7}{6},0\right\)) / (\left\(\frac{7}{6},0\right\)) and (\left\(-\frac{7}{6},0\right\))
B ((7,0)) और ((-7,0)) / ((7,0)) and ((-7,0))
C (\left\(\frac{6}{7},0\right\)) और (\left\(-\frac{6}{7},0\right\)) / (\left\(\frac{6}{7},0\right\)) and (\left\(-\frac{6}{7},0\right\))
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
A. (\left\(\frac{7}{6},0\right\)) और (\left\(-\frac{7}{6},0\right\)) / (\left\(\frac{7}{6},0\right\)) and (\left\(-\frac{7}{6},0\right\))
Step 1
Concept
From \(36x^2-49=0\), \(x=\pm\frac{7}{6}\). Tip: treat \(36x^2\) as ((6x)2 ).
Step 2
Why this answer is correct
The correct answer is A. (\left\(\frac{7}{6},0\right\)) और (\left\(-\frac{7}{6},0\right\)) / (\left\(\frac{7}{6},0\right\)) and (\left\(-\frac{7}{6},0\right\)). From \(36x^2-49=0\), \(x=\pm\frac{7}{6}\). Tip: treat \(36x^2\) as ((6x)2 ).
Step 3
Exam Tip
\(36x^2-49=0\) से \(x=\pm\frac{7}{6}\) मिलता है। टिप: \(36x^2\) को ((6x)2 ) समझें।
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Question 27/180
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=(x+9)(x-5)(x-12)) है, तो (5<x<12) में (p(x)) का चिह्न क्या होगा?
If (p(x)=(x+9)(x-5)(x-12)), what will be the sign of (p(x)) for (5<x<12)?
#sign interval
#factor form
#graph
A धनात्मक / Positive
B ऋणात्मक / Negative
C शून्य / Zero
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
B. ऋणात्मक / Negative
Step 1
Concept
In this interval the first two factors are positive and the third is negative, so the product is negative. Tip: check the sign of each factor separately.
Step 2
Why this answer is correct
The correct answer is B. ऋणात्मक / Negative. In this interval the first two factors are positive and the third is negative, so the product is negative. Tip: check the sign of each factor separately.
Step 3
Exam Tip
इस अंतराल में पहले दो कारक धनात्मक और तीसरा ऋणात्मक है, इसलिए गुणनफल ऋणात्मक है। टिप: प्रत्येक कारक का चिह्न अलग जांचें।
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Question 28/180
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=x-2 -14x+53) है, तो ग्राफ (x)-अक्ष को क्यों नहीं काटेगा?
If (p(x)=x-2 -14x+53), why will the graph not cut the (x)-axis?
#complete square
#no real zero
#graph
A क्योंकि यह ((x-7)2 +4) है / Because it is ((x-7)2 +4)
B क्योंकि यह ((x-7)2 ) है / Because it is ((x-7)2 )
C क्योंकि इसके शून्यक (7) और (4) हैं / Because its zeroes are (7) and (4)
D क्योंकि यह स्थिर बहुपद है / Because it is a constant polynomial
Explanation opens after your attempt
Correct Answer
A. क्योंकि यह ((x-7)2 +4) है / Because it is ((x-7)2 +4)
Step 1
Concept
((x-7)2 +4) is always positive, so (p(x)=0) will not occur. Tip: adding a positive number to a square gives no real intersection.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि यह ((x-7)2 +4) है / Because it is ((x-7)2 +4). ((x-7)2 +4) is always positive, so (p(x)=0) will not occur. Tip: adding a positive number to a square gives no real intersection.
Step 3
Exam Tip
((x-7)2 +4) हमेशा धनात्मक है इसलिए (p(x)=0) नहीं होगा। टिप: वर्ग में धनात्मक संख्या जुड़ने पर वास्तविक कटान नहीं मिलता।
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Question 29/180
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=x-2 +20x+100) है, तो ग्राफ (x)-अक्ष को किस बिंदु पर स्पर्श करेगा?
If (p(x)=x-2 +20x+100), at which point will the graph touch the (x)-axis?
#perfect square
#touching point
#graph
A ((-10,0))
B ((10,0))
C ((20,0))
D ((0,100))
Explanation opens after your attempt
Correct Answer
A. ((-10,0))
Step 1
Concept
(x-2 +20x+100=(x+10)2 ), so the touching point is ((-10,0)). Tip: change the sign in a perfect square to get the zero.
Step 2
Why this answer is correct
The correct answer is A. ((-10,0)). (x-2 +20x+100=(x+10)2 ), so the touching point is ((-10,0)). Tip: change the sign in a perfect square to get the zero.
Step 3
Exam Tip
(x-2 +20x+100=(x+10)2 ) है, इसलिए स्पर्श बिंदु ((-10,0)) है। टिप: पूर्ण वर्ग में चिह्न बदलकर शून्यक मिलता है।
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Question 30/180
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=x-2 -13x-68) है, तो ग्राफ के (x)-अक्ष कटान कौन से हैं?
If (p(x)=x-2 -13x-68), what are the (x)-axis intersections of the graph?
#quadratic factorization
#intercepts
#graph
A ((17,0)) और ((-4,0)) / ((17,0)) and ((-4,0))
B ((-17,0)) और ((4,0)) / ((-17,0)) and ((4,0))
C ((0,17)) और ((0,-4)) / ((0,17)) and ((0,-4))
D ((68,0)) और ((-13,0)) / ((68,0)) and ((-13,0))
Explanation opens after your attempt
Correct Answer
A. ((17,0)) और ((-4,0)) / ((17,0)) and ((-4,0))
Step 1
Concept
(x-2 -13x-68=(x-17)(x+4)), so the zeroes are (17) and (-4). Tip: write intersection points from factors.
Step 2
Why this answer is correct
The correct answer is A. ((17,0)) और ((-4,0)) / ((17,0)) and ((-4,0)). (x-2 -13x-68=(x-17)(x+4)), so the zeroes are (17) and (-4). Tip: write intersection points from factors.
Step 3
Exam Tip
(x-2 -13x-68=(x-17)(x+4)) है, इसलिए शून्यक (17) और (-4) हैं। टिप: गुणनखंडों से कटान बिंदु लिखें।
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