CBSE Class 10 Mathematics Polynomials Worksheet Set E

Multiple Choice Questions

Question. Sum of the zeroes of the polynomial x² + 7x + 10 are
(a) 7
(b) – 7
(c) 10
(d) – 10
Answer : B

Question. Quadratic polynomial having zeroes a and b is
(a) x² – (ab)x + (a + b)
(b) x² – (a + b)x + ab
(c) x² − (a/b) x + ab
(d) None of these
Answer : B

Question. If one zero of the quadratic polynomial x² – 5x – 6 is 6, then other zero is
(a) 0
(b) 1
(c) –1
(d) 2
Answer : C

Question. If the sum of the zeroes of the quadratic polynomial 3x² – kx + 6 is 3, then the value of k is
(a) 3
(b) 6
(c) 9
(d) 0
Answer : C

Question. A teacher asked 10 of his students to write a polynomial in one variable on a paper and then to handover the paper. The following were the answers given by the students:
2x + 3, 3x² + 7x + 2, 4x³ + 3x² + 2, x3 + √3x + 7, 7x + √7 , 5x³ – 7x + 2, 2x² + 3 – 5/x, 5x – 1/2, ax³ + bx² + cx + d, x + 1/x
How many of the above ten, are not polynomials?
(a) 1
(b) 2
(c) 3
(d) 4
Answer : C

Question. How many of the above ten (in question 12), are quadratic polynomials?
(a) 0
(b) 1
(c) 2
(d) 3
Answer : B

Question. A quadratic polynomial, whose sum of zeroes is 2 and product is –8 is
(a) x² – 3x – 3
(b) x² + 2x + 8
(c) x² + 3x + 3
(d) x² – 2x – 8
Answer : D

Question. The zeores of the quadratic polynomial 6x² – 3 – 7x are
(a) 3/2, -1/3
(b) 2/3, –3
(c) 3/5, -3/7
(d) None of these
Answer : A

Question. Which of the following is not the graph of a quadratic polynomial?

Answer : D

Question. The value of p, for which (–4) is a zero of the polynomial x² – 2x – (7p + 3) is
(a) 0
(b) 2
(c) 3
(d) None of these
Answer : C

Question. The zeroes of the quadratic polynomial 4x² – 4x – 3 are
(a) 3/2, -1/3
(b) 3/2, -1/2
(c) 2/5, -2/5
(d) None of these
Answer : B

Question. What number should be added to the polynomial x² – 5x + 4, so that 3 is the zero of the polynomial?
(a) 0
(b) 1
(c) 2
(d) 3
Answer : C

Question. A quadratic polynomial, the sum and product of whose zeroes and (–3) and 2 respectively is
(a) x² + 3x + 2
(b) x² – 3x + 2
(c) x² + 3x – 2
(d) None of these
Answer : A

Question. A quadratic polynomial whose zeroes are 5 − 3 2 and 5 + 3 2 is
(a) x² – 10x + 7
(b) x² + 10x + 7
(c) x² – 5x + 9
(d) x² + 5x – 9
Answer : A

Question. If 2 is a zero of the polynomial ax² – 2x, then the value of ‘a’ is
(a) 3
(b) 1
(c) 2
(d) 5
Answer : B

Question. The quadratic polynomial, the sum of whose zeroes is –5 and their product is 6, is
(a) x² + 5x + 6
(b) x² – 5x + 6
(c) x² – 5x – 6
(d) –x² + 5x + 6
Answer : A

Question. The zeroes of the quadratic polynomial x² + 7x + 10 are
(a) –2, –5
(b) 2, 5
(c) –3, –8
(d) 3, 8
Answer : A

Question. For what value of k, (– 4) is a zero of p(x) = x² – x – (2k – 2)?
(a) 8
(b) 11
(c) 13
(d) 15
Answer : B
 

B. Assertion-Reason Type Questions

In the following questions, a statement of assertion (A) is followed by a statement reason (R). Choose the correct choice as:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Question. Assertion (A): x² + 4x + 5 has two zeroes.
Reason (R): A quadratic polynomial can have at the most two zeroes.
Answer : D

Question. Assertion (A): A quadratic polynomial whose zeroes are 5 + √2 and 5 – √2 is x² – 10 x + 23.
Reason (R): If a and b are zeroes of the quadratic polynomial p(x), then p(x) = x² – (a + b) x + ab.
Answer : A

Question. Assertion (A): If one zero of polynomial p(x) = (k² + 4)x² + 13x + 4k is reciprocal of each other, then k = 2.
Reason (R): If (x – a) is a factor of p(x), then p(a) = 0, i.e. a is a zero of p(x).
Answer : B

Question. Assertion (A): If both zeroes of the quadratic polynomial x² –2kx + 2 are equal in magnitude but opposite in sign, then value of k is 1/2.
Reason (R): Sum of zeroes of a quadratic polynomial ax² + bx + c is − b/a
Answer : D

Please click the below link to access CBSE Class 10 Maths Worksheet - Polynomials (4)