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RD Chapter 2 Polynomials Ex MCQS Solutions

Question - 31 : -

The number of polynomials having zeroes -2 and 5 is
(a) 1
(b) 2
(c) 3
(d) more than 3

Answer - 31 : - (d)


Hence, the required number of polynomials are infinite i.e.,more than 3.

Question - 32 : -

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

Answer - 32 : - (a)


Question - 33 : -

The zeroes of the quadratic polynomial x2 + 99x + 127 are
(a) both positive
(b) both negative
(c) both equal
(d) one positive and one negative

Answer - 33 : - (b)



Question - 34 : -

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 - 34 : - (d)


Question - 35 : -

Given that one of the zeroes of the cubic polynomial ax3 + bx2 + cx + d is zero, the product of the othertwo zeroes is

Answer - 35 : - (b)


Question - 36 : -

The zeroes of the quadratic polynomial x2 + ax + a, a ≠ 0,
(a) cannot both be positive
(b) cannot both be negative
(c) area always unequal
(d) are always equal

Answer - 36 : -

(a) Let p(x) = x2 + ax + a, a ≠ 0
On comparing p(x) with ax2 + bx + c, we get
a = 1, b = a and c = a


So,both zeroes are negative.
Hence, in any case zeroes of the given quadratic polynomial cannot both thepositive.

Question - 37 : -

If one of the zeroes of the cubic polynomial x3 + ax2 + bx + c is -1, then the product of othertwo zeroes is
(a) b – a + 1
(b) b – a – 1
(c) a – b + 1
(d) a – b – 1

Answer - 37 : - (a)




Question - 38 : -

Given that two of the zeroes of the cubic polynomial ax3 + bx2 + cx + d are 0, the third zero is

Answer - 38 : -

(a) Two of the zeroes of the cubic polynomial
ax3 + bx2 + cx + d = 0, 0
Let the third zero be d
Then, use the relation between zeroes andcoefficient of polynomial, we have


Question - 39 : -

If one zero of the quadratic polynomial x2 + 3x + k is 2, then the value of k is
(a) 10
(b) -10
(c) 5
(d) -5

Answer - 39 : -

(b) Let the given quadratic polynomial be P(x) = x2 + 3x + k
It is given that one of its zeros is 2
P(2) = 0
=> (2)2 + 3(2) + k = 0=> 4 + 6 + k = 0
=> k + 10 = 0 => k = -10

Question - 40 : -

If the zeroes of the quadratic polynomial ax2 + bx + c, c ≠ 0 are 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 - 40 : -

(c) The zeroes of the given quadratic polynomialax2 + bx + c, c ≠ 0 are equal. If coefficient of x2 and constant term have the same sign
i.e., c and a have the same sign. While b i.e.,coefficient of x can be positive/negative but not zero.


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