The zeroes of the quadratic polynomial x2 + kx + k, k ≠ 0, (A) cannot both be positive (B) - Maths - Polynomials

Question

The zeroes of the quadratic polynomial x2 + kx + k, k ≠
0,
(A) cannot both be positive (B) cannot both be negative
(C) are always unequal (D) are always equal

Shridhar Kaushik · Accepted Answer

Given quadratic polynomial is

$p (x) = x^{2} + k x + k$

To find the nature of zeroes of the polynomial, we find discriminant (D) as follows:

${D = k}^{2} - 4 \times 1 \times k = k^{2} - 4 k = k (k - 4)$

For k ≠ 0, D can never be zero.

So the zeroes of the quadratic polynomial are always unequal.

The zeroes of the quadratic polynomial x2 + kx + k, k ≠ 0, (A) cannot both be positive (B) cannot both be negative (C) are always unequal (D) are always equal

The zeroes of the quadratic polynomial x2 + kx + k, k ≠ 0,

(A) cannot both be positive (B) cannot both be negative

(C) are always unequal (D) are always equal