Question 1/8
Hard Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 26
यदि (p(x)=x-3 -3x), तो (p\(\sqrt{3}\)) का मान क्या है?
If (p(x)=x-3 -3x), what is (p\(\sqrt{3}\))?
#cubic
#polynomial zero
#irrational
A (0)
B (3)
C \(3\sqrt{3}\)
D \(-3\sqrt{3}\)
Explanation opens after your attempt
Step 1
Concept
(\(\sqrt{3}\)3 =3\sqrt{3}), so \(3\sqrt{3}-3\sqrt{3}=0\). Simplifying powers is the key step in such questions.
Step 2
Why this answer is correct
The correct answer is A. (0). (\(\sqrt{3}\)3 =3\sqrt{3}), so \(3\sqrt{3}-3\sqrt{3}=0\). Simplifying powers is the key step in such questions.
Step 3
Exam Tip
(\(\sqrt{3}\)3 =3\sqrt{3}), इसलिए \(3\sqrt{3}-3\sqrt{3}=0\) है। परीक्षा में ऐसे प्रश्नों में घात को सरल करना मुख्य कदम है।
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Question 2/8
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि बहुपद (p(x)=5(x+1)(x-2)(x-4)) है तो ग्राफ (x)-अक्ष को कितने अलग बिंदुओं पर काटेगा?
If (p(x)=5(x+1)(x-2)(x-4)), at how many distinct points will the graph cut the (x)-axis?
#cubic
#factor-form
#distinct-intercepts
A तीन / Three
B दो / Two
C एक / One
D पाँच / Five
Explanation opens after your attempt
Correct Answer
A. तीन / Three
Step 1
Concept
The factors give zeroes (-1), (2), and (4). Three distinct zeroes give three distinct (x)-intercepts.
Step 2
Why this answer is correct
The correct answer is A. तीन / Three. The factors give zeroes (-1), (2), and (4). Three distinct zeroes give three distinct (x)-intercepts.
Step 3
Exam Tip
गुणनखंडों से शून्यक (-1), (2), और (4) हैं। तीन अलग शून्यक तीन अलग (x)-प्रतिच्छेद देते हैं।
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Question 3/8
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
ग्राफ (x)-अक्ष को ((-2,0)), ((0,0)), और ((5,0)) पर काटता है। कौन सा कथन सही है?
The graph cuts the (x)-axis at ((-2,0)), ((0,0)), and ((5,0)). Which statement is correct?
#multiple-zeroes
#origin
#cubic
A शून्यक (-2,0,5) हैं / The zeroes are (-2,0,5)
B शून्यक केवल (-2) और (5) हैं / The zeroes are only (-2) and (5)
C शून्यक ((0,0)) नहीं हो सकता / ((0,0)) cannot give a zero
D शून्यकों की संख्या दो है / The number of zeroes is two
Explanation opens after your attempt
Correct Answer
A. शून्यक (-2,0,5) हैं / The zeroes are (-2,0,5)
Step 1
Concept
The origin also lies on the (x)-axis so (0) is also a zero. Write the (x)-values of all intercepts.
Step 2
Why this answer is correct
The correct answer is A. शून्यक (-2,0,5) हैं / The zeroes are (-2,0,5). The origin also lies on the (x)-axis so (0) is also a zero. Write the (x)-values of all intercepts.
Step 3
Exam Tip
मूल बिंदु भी (x)-अक्ष पर है इसलिए (0) भी शून्यक है। सभी (x)-प्रतिच्छेदों के (x)-मान लिखें।
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Question 4/8
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 5/8
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि (p(x)=x-3 -25x) है तो ग्राफ (x)-अक्ष को कितने अलग बिंदुओं पर काटेगा?
If (p(x)=x-3 -25x), at how many distinct points will the graph cut the (x)-axis?
#cubic
#distinct 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
(x-3 -25x=x(x-5)(x+5)), so there are three distinct zeroes. Tip: first take out the common factor.
Step 2
Why this answer is correct
The correct answer is C. तीन / Three. (x-3 -25x=x(x-5)(x+5)), so there are three distinct zeroes. Tip: first take out the common factor.
Step 3
Exam Tip
(x-3 -25x=x(x-5)(x+5)) है इसलिए तीन अलग शून्यक हैं। टिप: पहले सामान्य गुणनखंड निकालें।
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Question 6/8
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=x-3 -16x) है, तो ग्राफ (x)-अक्ष को कितने अलग बिंदुओं पर काटेगा?
If (p(x)=x-3 -16x), at how many distinct points will the graph cut the (x)-axis?
#cubic
#distinct 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
(x-3 -16x=x(x-4)(x+4)), so there are three distinct zeroes. Tip: first take out the common factor.
Step 2
Why this answer is correct
The correct answer is C. तीन / Three. (x-3 -16x=x(x-4)(x+4)), so there are three distinct zeroes. Tip: first take out the common factor.
Step 3
Exam Tip
(x-3 -16x=x(x-4)(x+4)) है, इसलिए तीन अलग शून्यक हैं। टिप: पहले सामान्य गुणनखंड निकालें।
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Question 7/8
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 8/8
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(x)=x-3 -9x) है, तो ग्राफ (x)-अक्ष को कितने अलग बिंदुओं पर काट सकता है?
If (p(x)=x-3 -9x), at how many distinct points can the graph cut the (x)-axis?
#cubic
#distinct 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
(x-3 -9x=x(x-3)(x+3)), so there are three distinct zeroes. Tip: take the common factor and use difference of squares.
Step 2
Why this answer is correct
The correct answer is C. तीन / Three. (x-3 -9x=x(x-3)(x+3)), so there are three distinct zeroes. Tip: take the common factor and use difference of squares.
Step 3
Exam Tip
(x-3 -9x=x(x-3)(x+3)), इसलिए तीन अलग शून्यक हैं। टिप: सामान्य गुणनखंड निकालकर वर्गों का अंतर देखें।
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