Maths Polynomials 2

Question 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 1

Answer: (B)

Question 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 2

Answer: (C)

Question 3

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

(A) 1

(B) 2

(C) 3

(D) more than 3

Answer 3

Answer: (D)

Question 4

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

(A)2

(B) 3

(C) 4

(D) 5

Answer 4

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.

Question 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 5

Answer: (D)

Question 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 6

Answer: (B)

Question 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 7

Answer: (A)

Question 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 8

Answer: (A)

Question 9

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 9

Answer: (D)

Question 10

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 10

Answer: (D)

Question 11

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 11

Answer: (A)

Question 12

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 12

Answer: (A)

Question 13

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 13

Answer: (A)

Question 14

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 14

Answer: (A)