15 results found for "conjugate-zeroes" in Class 10.
Question
Expert Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 27
यदि परिमेय गुणांकों वाले द्विघात बहुपद का एक शून्यक \(4+\sqrt{11}\) है, तो दूसरा शून्यक कौन सा होगा?
If one zero of a quadratic polynomial with rational coefficients is \(4+\sqrt{11}\), what will be the other zero?
#conjugate-zeroes
#polynomials
#irrational-roots
A \(4-\sqrt{11}\)
B \(-4+\sqrt{11}\)
C \(\sqrt{11}-4\)
D \(4+\sqrt{11}\)
Explanation opens after your attempt
Correct Answer
A. \(4-\sqrt{11}\)
Step 1
Concept
With rational coefficients \(a+\sqrt{b}\) is accompanied by \(a-\sqrt{b}\). In exams identify conjugate zeroes quickly.
Step 2
Why this answer is correct
The correct answer is A. \(4-\sqrt{11}\). With rational coefficients \(a+\sqrt{b}\) is accompanied by \(a-\sqrt{b}\). In exams identify conjugate zeroes quickly.
Step 3
Exam Tip
परिमेय गुणांकों में \(a+\sqrt{b}\) के साथ \(a-\sqrt{b}\) भी शून्यक होता है। परीक्षा में संयुग्मी शून्यक तुरंत पहचानें।
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Question
Expert Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 26
यदि \(2+\sqrt{3}\) किसी परिमेय गुणांक वाले बहुपद का शून्यक है, तो किस रैखिक गुणनखंड का साथ आना अपेक्षित है?
If \(2+\sqrt{3}\) is a zero of a polynomial with rational coefficients, which linear factor is expected to accompany it?
#factor-theorem
#conjugate-zeroes
#polynomials
A (x-\(2-\sqrt{3}\))
B (x-\(2+\sqrt{3}\)) ही केवल / (x-\(2+\sqrt{3}\)) only
C (x-\(\sqrt{3}-2\))
D (x+\(2+\sqrt{3}\))
Explanation opens after your attempt
Correct Answer
A. (x-\(2-\sqrt{3}\))
Step 1
Concept
The companion zero is \(2-\sqrt{3}\), so the factor is (x-\(2-\sqrt{3}\)). In exams remember the relation between a zero and factor as \(x-\alpha\).
Step 2
Why this answer is correct
The correct answer is A. (x-\(2-\sqrt{3}\)). The companion zero is \(2-\sqrt{3}\), so the factor is (x-\(2-\sqrt{3}\)). In exams remember the relation between a zero and factor as \(x-\alpha\).
Step 3
Exam Tip
साथी शून्यक \(2-\sqrt{3}\) होगा, इसलिए गुणनखंड (x-\(2-\sqrt{3}\)) है। परीक्षा में शून्यक और गुणनखंड का संबंध \(x-\alpha\) याद रखें।
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Question
Expert Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 26
यदि किसी बहुपद का एक शून्यक \(\sqrt{11}\) है और गुणांक परिमेय हैं, तो कौन सा शून्यक भी होना चाहिए?
If one zero of a polynomial is \(\sqrt{11}\) and the coefficients are rational, which zero should also occur?
#conjugate-zeroes
#polynomials
#irrational-roots
A -\(\sqrt{11}\)
B (11)
C \(\frac{1}{\sqrt{11}}\)
D \(1+\sqrt{11}\)
Explanation opens after your attempt
Correct Answer
A. -\(\sqrt{11}\)
Step 1
Concept
The conjugate of \(\sqrt{11}=0+\sqrt{11}\) is \(-\sqrt{11}\). In exams also identify the case (a=0).
Step 2
Why this answer is correct
The correct answer is A. -\(\sqrt{11}\). The conjugate of \(\sqrt{11}=0+\sqrt{11}\) is \(-\sqrt{11}\). In exams also identify the case (a=0).
Step 3
Exam Tip
\(\sqrt{11}=0+\sqrt{11}\) का संयुग्मी \(-\sqrt{11}\) है। परीक्षा में (a=0) वाला संयुग्मी भी पहचानें।
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Question
Expert Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 26
कौन सा बहुपद \(1+\sqrt{6}\) और \(1-\sqrt{6}\) को शून्यक रखता है?
Which polynomial has \(1+\sqrt{6}\) and \(1-\sqrt{6}\) as zeroes?
#polynomial-formation
#conjugate-zeroes
#expert
A \(x^2-2x-5\)
B \(x^2+2x-5\)
C \(x^2-2x+5\)
D \(x^2+x-6\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-2x-5\)
Step 1
Concept
The sum is (2) and the product is (1-6=-5), so the polynomial is \(x^2-2x-5\). In exams use \(a^2-b^2\) for the product.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-2x-5\). The sum is (2) and the product is (1-6=-5), so the polynomial is \(x^2-2x-5\). In exams use \(a^2-b^2\) for the product.
Step 3
Exam Tip
योग (2) और गुणनफल (1-6=-5) है, इसलिए बहुपद \(x^2-2x-5\) है। परीक्षा में गुणनफल में \(a^2-b^2\) लगाएं।
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Question
Expert Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
यदि \(x^2+px+q\) के शून्यक \(7+2\sqrt{3}\) और \(7-2\sqrt{3}\) हैं, तो (p+q) क्या है?
If the zeroes of \(x^2+px+q\) are \(7+2\sqrt{3}\) and \(7-2\sqrt{3}\), what is (p+q)?
#parameter
#conjugate-zeroes
#sum-product
A (23)
B (37)
C (49)
D (61)
Explanation opens after your attempt
Step 1
Concept
The sum is (14), so (p=-14), and the product is (49-12=37), so (q=37). Hence (p+q=23).
Step 2
Why this answer is correct
The correct answer is A. (23). The sum is (14), so (p=-14), and the product is (49-12=37), so (q=37). Hence (p+q=23).
Step 3
Exam Tip
योग (14) है, इसलिए (p=-14), और गुणनफल (49-12=37) है, इसलिए (q=37)। अतः (p+q=23) है।
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Question
Expert Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
यदि किसी एकक द्विघात बहुपद के शून्यक \(4+\sqrt{11}\) और \(4-\sqrt{11}\) हैं, तो स्थिर पद क्या होगा?
If the zeroes of a monic quadratic polynomial are \(4+\sqrt{11}\) and \(4-\sqrt{11}\), what will be the constant term?
#conjugate-zeroes
#constant-term
#quadratic
A (5)
B (27)
C (8)
D \(16+\sqrt{11}\)
Explanation opens after your attempt
Step 1
Concept
The constant term is the product, and (\(4+\sqrt{11}\)\(4-\sqrt{11}\)=16-11=5). In conjugate products, the irrational middle part cancels.
Step 2
Why this answer is correct
The correct answer is A. (5). The constant term is the product, and (\(4+\sqrt{11}\)\(4-\sqrt{11}\)=16-11=5). In conjugate products, the irrational middle part cancels.
Step 3
Exam Tip
स्थिर पद गुणनफल है और (\(4+\sqrt{11}\)\(4-\sqrt{11}\)=16-11=5)। संयुग्मी गुणनफल में बीच का अपरिमेय भाग हट जाता है।
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Question
Hard Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 27
यदि किसी द्विघात बहुपद के शून्यक \(5+\sqrt{2}\) और \(5-\sqrt{2}\) हैं, तो बहुपद क्या होगा?
If the zeroes of a quadratic polynomial are \(5+\sqrt{2}\) and \(5-\sqrt{2}\), what is the polynomial?
#conjugate-zeroes
#polynomial-formation
#irrational
A \(x^2-10x+23\)
B \(x^2+10x+23\)
C \(x^2-10x+27\)
D \(x^2+10x-23\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-10x+23\)
Step 1
Concept
The sum is (10) and the product is (25-2=23). Therefore the polynomial is \(x^2-10x+23\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-10x+23\). The sum is (10) and the product is (25-2=23). Therefore the polynomial is \(x^2-10x+23\).
Step 3
Exam Tip
योग (10) और गुणनफल (25-2=23) है। इसलिए बहुपद \(x^2-10x+23\) होगा।
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Question
Hard Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 26
यदि किसी परिमेय गुणांकों वाले द्विघात बहुपद का एक शून्यक \(6-2\sqrt{5}\) है, तो उस बहुपद का एक संभव रूप क्या है?
If one zero of a quadratic polynomial with rational coefficients is \(6-2\sqrt{5}\), what is one possible form of that polynomial?
#conjugate-zeroes
#polynomial-formation
#final
A \(x^2-12x+16\)
B \(x^2-6x+20\)
C \(x^2+12x+16\)
D \(x^2-12x+20\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-12x+16\)
Step 1
Concept
The other zero is \(6+2\sqrt{5}\). The sum is (12) and product is (36-20=16), so the polynomial is \(x^2-12x+16\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-12x+16\). The other zero is \(6+2\sqrt{5}\). The sum is (12) and product is (36-20=16), so the polynomial is \(x^2-12x+16\).
Step 3
Exam Tip
दूसरा शून्यक \(6+2\sqrt{5}\) होगा। योग (12) और गुणनफल (36-20=16), इसलिए बहुपद \(x^2-12x+16\) है।
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Question
Hard Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 26
किस विकल्प में दिया बहुपद परिमेय गुणांकों वाला है और उसके शून्यक अपरिमेय संयुग्मी हैं?
Which option gives a polynomial with rational coefficients and irrational conjugate zeroes?
#rational-coefficients
#irrational-conjugates
#mcq
A \(x^2-6x+7\)
B \(x^2-\sqrt{2}x+1\)
C \(x^2-4x+4\)
D \(x^2+1\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-6x+7\)
Step 1
Concept
For \(x^2-6x+7\), (D=36-28=8). The coefficients are rational and the zeroes are \(3\pm\sqrt{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-6x+7\). For \(x^2-6x+7\), (D=36-28=8). The coefficients are rational and the zeroes are \(3\pm\sqrt{2}\).
Step 3
Exam Tip
\(x^2-6x+7\) में (D=36-28=8) है। गुणांक परिमेय हैं और शून्यक \(3\pm\sqrt{2}\) होंगे।
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Question
Hard Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 26
यदि (x-2 -2ax+\(a^2-5\)=0) के शून्यक \(a+\sqrt{5}\) और \(a-\sqrt{5}\) हैं, तो यह किस कारण सही है?
If zeroes of (x-2 -2ax+\(a^2-5\)=0) are \(a+\sqrt{5}\) and \(a-\sqrt{5}\), why is it correct?
#general-form
#conjugate-zeroes
#reasoning
A योग (2a) और गुणनफल \(a^2-5\) हैं / Sum is (2a) and product is \(a^2-5\)
B योग (a) और गुणनफल (5) हैं / Sum is (a) and product is (5)
C योग \(\sqrt{5}\) और गुणनफल \(a^2\) हैं / Sum is \(\sqrt{5}\) and product is \(a^2\)
D योग (0) और गुणनफल (-5) हैं / Sum is (0) and product is (-5)
Explanation opens after your attempt
Correct Answer
A. योग (2a) और गुणनफल \(a^2-5\) हैं / Sum is (2a) and product is \(a^2-5\)
Step 1
Concept
(\(a+\sqrt{5}\)+\(a-\sqrt{5}\)=2a) and (\(a+\sqrt{5}\)\(a-\sqrt{5}\)=a-2 -5). These match the polynomial.
Step 2
Why this answer is correct
The correct answer is A. योग (2a) और गुणनफल \(a^2-5\) हैं / Sum is (2a) and product is \(a^2-5\). (\(a+\sqrt{5}\)+\(a-\sqrt{5}\)=2a) and (\(a+\sqrt{5}\)\(a-\sqrt{5}\)=a-2 -5). These match the polynomial.
Step 3
Exam Tip
(\(a+\sqrt{5}\)+\(a-\sqrt{5}\)=2a) और (\(a+\sqrt{5}\)\(a-\sqrt{5}\)=a-2 -5)। यही बहुपद से मेल खाता है।
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Question
Hard Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 26
यदि (p(x)=x-2 +px+q) के शून्यक \(7+\sqrt{13}\) और \(7-\sqrt{13}\) हैं, तो (p+q) क्या है?
If zeroes of (p(x)=x-2 +px+q) are \(7+\sqrt{13}\) and \(7-\sqrt{13}\), what is (p+q)?
#parameter
#conjugate-zeroes
#sum-product
A (22)
B (35)
C (49)
D (-14)
Explanation opens after your attempt
Step 1
Concept
The sum is (14), so (p=-14). The product is (49-13=36), so (q=36) and (p+q=22).
Step 2
Why this answer is correct
The correct answer is A. (22). The sum is (14), so (p=-14). The product is (49-13=36), so (q=36) and (p+q=22).
Step 3
Exam Tip
योग (14) है, इसलिए (p=-14)। गुणनफल (49-13=36) है, इसलिए (q=36) और (p+q=22)।
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Question
Hard Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 28
यदि किसी द्विघात बहुपद के परिमेय गुणांक हैं और शून्यक \(4+\sqrt{11}\) है, तो शून्यकों का योग क्या होगा?
If a quadratic polynomial has rational coefficients and one zero is \(4+\sqrt{11}\), what will be the sum of its zeroes?
#rational-coefficients
#conjugate-zeroes
#sum
A (8)
B (4)
C \(2\sqrt{11}\)
D (16-11)
Explanation opens after your attempt
Step 1
Concept
The other zero will be \(4-\sqrt{11}\). The sum is (\(4+\sqrt{11}\)+\(4-\sqrt{11}\)=8).
Step 2
Why this answer is correct
The correct answer is A. (8). The other zero will be \(4-\sqrt{11}\). The sum is (\(4+\sqrt{11}\)+\(4-\sqrt{11}\)=8).
Step 3
Exam Tip
दूसरा शून्यक \(4-\sqrt{11}\) होगा। योग (\(4+\sqrt{11}\)+\(4-\sqrt{11}\)=8) है।
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Question
Hard Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 28
किस बहुपद के शून्यक \(1+\sqrt{2}\) और \(1-\sqrt{2}\) हैं?
Which polynomial has zeroes \(1+\sqrt{2}\) and \(1-\sqrt{2}\)?
#polynomial-formation
#conjugate-zeroes
#irrational
A \(x^2-2x-1\)
B \(x^2+2x-1\)
C \(x^2-2x+1\)
D \(x^2+x-2\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-2x-1\)
Step 1
Concept
The sum is (2) and the product is (-1). So the polynomial is \(x^2-2x-1\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-2x-1\). The sum is (2) and the product is (-1). So the polynomial is \(x^2-2x-1\).
Step 3
Exam Tip
योग (2) और गुणनफल (-1) है। इसलिए बहुपद \(x^2-2x-1\) है।
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Question
Hard Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 28
यदि \(2+\sqrt{3}\) और \(2-\sqrt{3}\) किसी द्विघात बहुपद के शून्यक हैं, तो बहुपद क्या होगा?
If \(2+\sqrt{3}\) and \(2-\sqrt{3}\) are zeroes of a quadratic polynomial, what is the polynomial?
#conjugate-zeroes
#polynomial-formation
#real-numbers
A \(x^2-4x+1\)
B \(x^2+4x+1\)
C \(x^2-2x+3\)
D \(x^2+2x-3\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-4x+1\)
Step 1
Concept
The sum is (4) and the product is (1). Therefore the polynomial is \(x^2-4x+1\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-4x+1\). The sum is (4) and the product is (1). Therefore the polynomial is \(x^2-4x+1\).
Step 3
Exam Tip
योग (4) और गुणनफल (1) है। अतः बहुपद \(x^2-4x+1\) है।
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Question
Hard Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 28
यदि किसी द्विघात बहुपद के परिमेय गुणांक हैं और एक शून्यक \(3+\sqrt{5}\) है, तो दूसरा शून्यक क्या होगा?
If a quadratic polynomial has rational coefficients and one zero is \(3+\sqrt{5}\), what will be the other zero?
#polynomials
#conjugate-zeroes
#irrational-roots
A \(3-\sqrt{5}\)
B \(-3+\sqrt{5}\)
C \(5-\sqrt{3}\)
D \(-3-\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(3-\sqrt{5}\)
Step 1
Concept
For a quadratic with rational coefficients, \(a-\sqrt{b}\) accompanies \(a+\sqrt{b}\). Remember this as the conjugate-zero rule.
Step 2
Why this answer is correct
The correct answer is A. \(3-\sqrt{5}\). For a quadratic with rational coefficients, \(a-\sqrt{b}\) accompanies \(a+\sqrt{b}\). Remember this as the conjugate-zero rule.
Step 3
Exam Tip
परिमेय गुणांकों वाले द्विघात में \(a+\sqrt{b}\) के साथ \(a-\sqrt{b}\) भी शून्यक होता है। परीक्षा में इसे संयुग्मी शून्यक नियम की तरह याद रखें।
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