CBSE Class 10 Maths Standard Relationship Between Zeroes and Coefficients Competency Based Questions

Topic-wise competency based questions from Polynomials. Attempt first, then open the answer and solution.

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CBQs Important Questions PYQs

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Question 1MCQ · Apply · 1 mark

Polynomials · Relationship Between Zeroes and Coefficients

$x^{2} + (a + b) x + b$ has zeros $2$ and $- 5$ . Find $(a, b)$ .

(A) $(13, - 10)$ (B) $(- 13, 10)$ (C) $(3, - 10)$ (D) $(13, 10)$

Open answer and solution

Answer

(A) $(13, - 10)$

Solution

The sum is $- 3$ , so $a + b = 3$ . The product is $- 10$ , so $b = - 10$ , giving $a = 13$ .

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Question 2MCQ · Apply · 1 mark

Polynomials · Relationship Between Zeroes and Coefficients

Which monic polynomial has zeros summing to $- 3$ and multiplying to $- 10$ ? (A) $x^{2} - 3 x - 10$ (B) $x^{2} + 3 x + 10$ (C) $x^{2} + 3 x - 10$ (D) $x^{2} - 3 x + 10$

Open answer and solution

Answer

Solution

Use $x^{2} - (e x t s u m) x + e x t p r o d u c t = x^{2} + 3 x - 10$ .

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Question 3MCQ · Apply · 1 mark

Polynomials · Relationship Between Zeroes and Coefficients

If $f (x) = a x^{2} + b x + c$ , $f (0) = 4$ , $f (1) = 9$ , $f (- 1) = 3$ , then $f (x)$ is: (A) $x^{2} + 4 x + 4$ (B) $2 x^{2} + 3 x + 4$ (C) $3 x^{2} + 2 x + 4$ (D) $2 x^{2} - 3 x + 4$

Open answer and solution

Answer

(B) $2 x^{2} + 3 x + 4$

Solution

$c = 4$ , $a + b = 5$ , and $a - b = - 1$ . Thus $a = 2, b = 3$ .

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Question 4MCQ · Apply · 1 mark

Polynomials · Relationship Between Zeroes and Coefficients

The sum of zeros of $3 x^{2} - k x + 1$ is $4$ . Find $k$ . (A) $3$ (B) $6$ (C) $9$ (D) $12$

Open answer and solution

Answer

(D) $12$

Solution

Sum is $k /3 = 4$ , hence $k = 12$ .

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Question 5MCQ · Analyse · 1 mark

Polynomials · Relationship Between Zeroes and Coefficients

Zeros $alpha,eta$ of $2 x^{2} + 6 x + k$ satisfy $alpha^2+eta^2+alphaeta=7$ . Find $k$ . (A) $2$ (B) $4$ (C) $6$ (D) $8$

Open answer and solution

Answer

(B) $4$

Solution

Sum is $- 3$ and product $k /2$ . The expression is $9 - k /2 = 7$ , so $k = 4$ .

Mark as completed

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CBSE Class 10 Maths Standard Relationship Between Zeroes and Coefficients Competency Based Questions

Topic-wise competency based questions from Polynomials. Attempt first, then open the answer and solution.

ChapterTopic

CBSE Class 10 Maths Standard Relationship Between Zeroes and Coefficients Competency Based Questions

x2+(a+b)x+b has zeros 2 and −5. Find (a,b).(A) (13,−10) (B) (−13,10) (C) (3,−10) (D) (13,10)

Which monic polynomial has zeros summing to −3 and multiplying to −10? (A) x2−3x−10 (B) x2+3x+10 (C) x2+3x−10 (D) x2−3x+10

If f(x)=ax2+bx+c, f(0)=4, f(1)=9, f(−1)=3, then f(x) is: (A) x2+4x+4 (B) 2x2+3x+4 (C) 3x2+2x+4 (D) 2x2−3x+4

The sum of zeros of 3x2−kx+1 is 4. Find k. (A) 3 (B) 6 (C) 9 (D) 12

Zeros alpha,eta of 2x2+6x+k satisfy alpha^2+eta^2+alphaeta=7. Find k. (A) 2 (B) 4 (C) 6 (D) 8

CBSE Class 10 Maths Standard Relationship Between Zeroes and Coefficients Competency Based Questions

x2+(a+b)x+b has zeros 2 and −5. Find (a,b).(A) (13,−10) (B) (−13,10) (C) (3,−10) (D) (13,10)

Which monic polynomial has zeros summing to −3 and multiplying to −10? (A) x2−3x−10 (B) x2+3x+10 (C) x2+3x−10 (D) x2−3x+10

If f(x)=ax2+bx+c, f(0)=4, f(1)=9, f(−1)=3, then f(x) is: (A) x2+4x+4 (B) 2x2+3x+4 (C) 3x2+2x+4 (D) 2x2−3x+4

The sum of zeros of 3x2−kx+1 is 4. Find k. (A) 3 (B) 6 (C) 9 (D) 12

Zeros alpha,eta of 2x2+6x+k satisfy alpha^2+eta^2+alphaeta=7. Find k. (A) 2 (B) 4 (C) 6 (D) 8

$x^{2} + (a + b) x + b$ has zeros $2$ and $- 5$ . Find $(a, b)$ .

(A) $(13, - 10)$ (B) $(- 13, 10)$ (C) $(3, - 10)$ (D) $(13, 10)$

Which monic polynomial has zeros summing to $- 3$ and multiplying to $- 10$ ? (A) $x^{2} - 3 x - 10$ (B) $x^{2} + 3 x + 10$ (C) $x^{2} + 3 x - 10$ (D) $x^{2} - 3 x + 10$

If $f (x) = a x^{2} + b x + c$ , $f (0) = 4$ , $f (1) = 9$ , $f (- 1) = 3$ , then $f (x)$ is: (A) $x^{2} + 4 x + 4$ (B) $2 x^{2} + 3 x + 4$ (C) $3 x^{2} + 2 x + 4$ (D) $2 x^{2} - 3 x + 4$

The sum of zeros of $3 x^{2} - k x + 1$ is $4$ . Find $k$ . (A) $3$ (B) $6$ (C) $9$ (D) $12$

Zeros $alpha,eta$ of $2 x^{2} + 6 x + k$ satisfy $alpha^2+eta^2+alphaeta=7$ . Find $k$ . (A) $2$ (B) $4$ (C) $6$ (D) $8$

$x^{2} + (a + b) x + b$ has zeros $2$ and $- 5$ . Find $(a, b)$ .

(A) $(13, - 10)$ (B) $(- 13, 10)$ (C) $(3, - 10)$ (D) $(13, 10)$

Which monic polynomial has zeros summing to $- 3$ and multiplying to $- 10$ ? (A) $x^{2} - 3 x - 10$ (B) $x^{2} + 3 x + 10$ (C) $x^{2} + 3 x - 10$ (D) $x^{2} - 3 x + 10$

If $f (x) = a x^{2} + b x + c$ , $f (0) = 4$ , $f (1) = 9$ , $f (- 1) = 3$ , then $f (x)$ is: (A) $x^{2} + 4 x + 4$ (B) $2 x^{2} + 3 x + 4$ (C) $3 x^{2} + 2 x + 4$ (D) $2 x^{2} - 3 x + 4$

The sum of zeros of $3 x^{2} - k x + 1$ is $4$ . Find $k$ . (A) $3$ (B) $6$ (C) $9$ (D) $12$

Zeros $alpha,eta$ of $2 x^{2} + 6 x + k$ satisfy $alpha^2+eta^2+alphaeta=7$ . Find $k$ . (A) $2$ (B) $4$ (C) $6$ (D) $8$