Question 1/14
Expert Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 27
किस द्विघात बहुपद के शून्यक \(2+\sqrt{10}\) और \(2-\sqrt{10}\) हैं?
Which quadratic polynomial has zeroes \(2+\sqrt{10}\) and \(2-\sqrt{10}\)?
#polynomial-formation
#zeroes
#surds
A \(x^2-4x-6\)
B \(x^2+4x-6\)
C \(x^2-4x+6\)
D \(x^2-2x-10\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-4x-6\)
Step 1
Concept
The sum is (4) and the product is (4-10=-6). Hence the polynomial is \(x^2-4x-6\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-4x-6\). The sum is (4) and the product is (4-10=-6). Hence the polynomial is \(x^2-4x-6\).
Step 3
Exam Tip
योग (4) और गुणनफल (4-10=-6) है। इसलिए बहुपद \(x^2-4x-6\) होगा।
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Question 2/14
Expert Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 26
किस विकल्प में बहुपद के सभी गुणांक परिमेय हैं और शून्यक \(6+\sqrt{11}\) तथा \(6-\sqrt{11}\) हैं?
Which option has all rational coefficients and zeroes \(6+\sqrt{11}\) and \(6-\sqrt{11}\)?
#polynomial-formation
#irrational-zeroes
#conjugates
A \(x^2-12x+25\)
B \(x^2+12x+25\)
C \(x^2-6x+11\)
D \(x^2-12x+47\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-12x+25\)
Step 1
Concept
The sum is (12) and the product is (36-11=25), so the polynomial is \(x^2-12x+25\). In exams write the standard form correctly.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-12x+25\). The sum is (12) and the product is (36-11=25), so the polynomial is \(x^2-12x+25\). In exams write the standard form correctly.
Step 3
Exam Tip
योग (12) और गुणनफल (36-11=25) है, इसलिए बहुपद \(x^2-12x+25\) है। परीक्षा में मानक रूप ठीक से लिखें।
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Question 3/14
Expert Mathematics
Chapter 2: 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 4/14
Expert Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 26
किस द्विघात बहुपद के शून्यक \(3+\sqrt{2}\) और \(3-\sqrt{2}\) हैं?
Which quadratic polynomial has zeroes \(3+\sqrt{2}\) and \(3-\sqrt{2}\)?
#polynomial-formation
#surds
#zeroes
A \(x^2-6x+7\)
B \(x^2+6x+7\)
C \(x^2-3x+2\)
D \(x^2-6x+11\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-6x+7\)
Step 1
Concept
The sum is (6) and the product is (7), so the polynomial is \(x^2-6x+7\). In exams use (x-2 -(sum)x+product).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-6x+7\). The sum is (6) and the product is (7), so the polynomial is \(x^2-6x+7\). In exams use (x-2 -(sum)x+product).
Step 3
Exam Tip
योग (6) और गुणनफल (7) है, इसलिए बहुपद \(x^2-6x+7\) है। परीक्षा में (x-2 -(योग)x+गुणनफल) प्रयोग करें।
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Question 5/14
Expert Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 25
यदि शून्यक \(\frac{3+\sqrt{5}}{2}\) और \(\frac{3-\sqrt{5}}{2}\) हैं, तो एकक बहुपद क्या है?
If the zeroes are \(\frac{3+\sqrt{5}}{2}\) and \(\frac{3-\sqrt{5}}{2}\), what is the monic polynomial?
#polynomial-formation
#fractional-conjugates
#irrational
A \(x^2-3x+1\)
B \(x^2+3x+1\)
C \(x^2-3x-1\)
D \(x^2-\frac{3}{2}x+1\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-3x+1\)
Step 1
Concept
The sum is (3) and the product is \(\frac{9-5}{4}=1\). Therefore the polynomial is \(x^2-3x+1\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-3x+1\). The sum is (3) and the product is \(\frac{9-5}{4}=1\). Therefore the polynomial is \(x^2-3x+1\).
Step 3
Exam Tip
योग (3) और गुणनफल \(\frac{9-5}{4}=1\) है। इसलिए बहुपद \(x^2-3x+1\) है।
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Question 6/14
Expert Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 25
किस बहुपद के शून्यक \(3+\sqrt{2}\) और \(3-\sqrt{2}\) हैं?
Which polynomial has zeroes \(3+\sqrt{2}\) and \(3-\sqrt{2}\)?
#polynomial-formation
#conjugates
#irrational-roots
A \(x^2-6x+7\)
B \(x^2+6x+7\)
C \(x^2-6x+11\)
D \(x^2+6x-7\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-6x+7\)
Step 1
Concept
The sum is (6) and the product is (9-2=7). The polynomial is \(x^2-6x+7\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-6x+7\). The sum is (6) and the product is (9-2=7). The polynomial is \(x^2-6x+7\).
Step 3
Exam Tip
योग (6) और गुणनफल (9-2=7) है। बहुपद \(x^2-6x+7\) होगा।
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Question 7/14
Hard Mathematics
Chapter 2: 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 8/14
Hard Mathematics
Chapter 2: 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 9/14
Hard Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 26
किस बहुपद के शून्यकों का योग \(5\sqrt{2}\) और गुणनफल (12) है?
Which polynomial has zeroes with sum \(5\sqrt{2}\) and product (12)?
#polynomial-formation
#sum-product
#irrational
A \(x^2-5\sqrt{2}x+12\)
B \(x^2+5\sqrt{2}x+12\)
C \(x^2-12x+5\sqrt{2}\)
D \(x^2+12x-5\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-5\sqrt{2}x+12\)
Step 1
Concept
The polynomial is \(x^2-Sx+P\). Here \(S=5\sqrt{2}\) and (P=12).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-5\sqrt{2}x+12\). The polynomial is \(x^2-Sx+P\). Here \(S=5\sqrt{2}\) and (P=12).
Step 3
Exam Tip
बहुपद \(x^2-Sx+P\) होता है। यहाँ \(S=5\sqrt{2}\) और (P=12) हैं।
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Question 10/14
Hard Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 28
यदि शून्यकों का योग \(2\sqrt{5}\) और गुणनफल (4) है, तो एक मानक द्विघात बहुपद कौन सा होगा?
If the sum of zeroes is \(2\sqrt{5}\) and the product is (4), which is a monic quadratic polynomial?
#polynomial-formation
#sum-product
#irrational
A \(x^2-2\sqrt{5}x+4\)
B \(x^2+2\sqrt{5}x+4\)
C \(x^2-4x+2\sqrt{5}\)
D \(x^2+4x-2\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-2\sqrt{5}x+4\)
Step 1
Concept
A monic polynomial is (x-2 -(sum)x+product). So the answer is \(x^2-2\sqrt{5}x+4\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-2\sqrt{5}x+4\). A monic polynomial is (x-2 -(sum)x+product). So the answer is \(x^2-2\sqrt{5}x+4\).
Step 3
Exam Tip
मानक बहुपद (x-2 -(योग)x+गुणनफल) होता है। इसलिए उत्तर \(x^2-2\sqrt{5}x+4\) है।
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Question 11/14
Hard Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 28
किस बहुपद के शून्यक \(\sqrt{2}+\sqrt{3}\) और \(\sqrt{2}-\sqrt{3}\) हैं?
Which polynomial has zeroes \(\sqrt{2}+\sqrt{3}\) and \(\sqrt{2}-\sqrt{3}\)?
#polynomial-formation
#irrational-coefficients
#zeroes
A \(x^2-2\sqrt{2}x-1\)
B \(x^2-2\sqrt{3}x+1\)
C \(x^2+2\sqrt{2}x-1\)
D \(x^2-5\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-2\sqrt{2}x-1\)
Step 1
Concept
The sum is \(2\sqrt{2}\) and the product is (2-3=-1). Hence the polynomial is \(x^2-2\sqrt{2}x-1\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-2\sqrt{2}x-1\). The sum is \(2\sqrt{2}\) and the product is (2-3=-1). Hence the polynomial is \(x^2-2\sqrt{2}x-1\).
Step 3
Exam Tip
योग \(2\sqrt{2}\) और गुणनफल (2-3=-1) है। इसलिए बहुपद \(x^2-2\sqrt{2}x-1\) बनेगा।
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Question 12/14
Hard Mathematics
Chapter 2: 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 13/14
Hard Mathematics
Chapter 2: 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 14/14
Hard Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 28
किस बहुपद के शून्यक \(\sqrt{7}\) और \(-\sqrt{7}\) हैं?
Which polynomial has zeroes \(\sqrt{7}\) and \(-\sqrt{7}\)?
#zeroes
#polynomial-formation
#irrational-numbers
A \(x^2-7\)
B \(x^2+7\)
C \(x^2-2\sqrt{7}x+7\)
D \(x^2+2\sqrt{7}x-7\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-7\)
Step 1
Concept
The sum of zeroes is (0) and the product is (-7). Hence the polynomial is \(x^2-7\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-7\). The sum of zeroes is (0) and the product is (-7). Hence the polynomial is \(x^2-7\).
Step 3
Exam Tip
शून्यकों का योग (0) और गुणनफल (-7) है। इसलिए बहुपद \(x^2-7\) होगा।
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