1. The zeroes of the quadratic polynomial x² + 99x + 127are

(A) both positive                                            

(B) both negative

(C) one positive and one negative                 

(D) both equal

Answer: (B)

2. If the zeroes of the quadratic polynomial x² + bx + c , c ≠ 0are equal, then

(A) c and a have opposite signs

(B) c and b have opposite signs

(C) c and a have the same sign          

(D) c and b have the same sign

Answer: (C)

3. The number of polynomials having zeroes as –2 and 5 is

(A) 1                                                                     

(B) 2

(C) 3                                                                      

(D) more than 3

Answer:  (D)

4. The degree of the polynomial (x + 1)(x² – x – x⁴ +1) is:

(A)2                                                      

(B) 3

(C) 4                                                      

(D) 5

Answer:  (D)

Explanation: Since the highest degree variable in first bracket is x and in second bracket is x⁴ on multiplying x with x⁴.the highest power we obtain is 5.

5. If the zeroes of the quadratic polynomial x² + (a + 1)x + b are 2 and –3, then

(A) a = –7, b = –1                                                             

(B) a = 5, b = –1

(C) a = 2, b = – 6                                                               

(D) a = 0, b = – 6

Answer:  (D)

6. Given that one of the zeroes of the cubic polynomial ax³ + bx² + cx + d is zero, the product of the other two zeroes is

(A) –c/a                                                                               

(B) c/a

(C) 0                                                                                      

(D) 3

Answer:  (B)

7. If one of the zeroes of the cubic polynomial x³ + ax² + bx + c is –1, then the

Product of the other two zeroes is

(A) b – a + 1                                       

(B) b – a – 1

(C) a – b + 1                                       

(D) a – b –1

Answer: (A)

8. If one of the zeroes of the quadratic polynomial (k – 1)x² + kx + 1 is –3, then the value of k is

(A) 4/3                                                                 

(B) – 4/3

(C) 2/3                                                                 

(D) – 2/3

Answer:  (A)

10. The value of p for which the polynomial x³ + 4x² –px + 8 is exactly divisible by (x – 2) is: 

(A) 0                                                                                     

(B) 3

(C) 5                                                                                      

(D) 16 

Answer: (D)

11. If sum of the squares of zeroes of the quadratic polynomial 6x² + x + k is 25/36, the value of k is: 

(A) 4                                                                                     

(B) – 4

(C) 2                                                                                      

(D) – 2

Answer:  (D)

12. If α and β are zeroes of x² – 4x + 1, then 1/α + 1/β – αβ is 

(A) 3                                                                     

(B) 5

(C) –5

(D) –3 

Answer:  (A)

13. If (x + 1) is a factor of x²− 3ax +3a − 7, then the value of a is: 

(A) 1                                                                     

(B) –1

(C) 0                                                                      

(D) –2 

Answer: (A)

14. If one of the zeroes of a quadratic polynomial of the form x² + ax + b is the negative of the other, then it

(A) has no linear term and the constant term is negative.

(B) has no linear term and the constant term is positive.

(C) can have a linear term but the constant term is negative.

(D) can have a linear term but the constant term is positive

Answer: (A)

15. If α, β are zeroes of x² –6x + k, what is the value of k if 3α + 2β = 20? 

(A)–16                                                 

(B) 8

(C) 2                                                                      

(D) –8 

Answer: (A)

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MCQs: Polynomials

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