Question

Find the value of ‘k’ for which the equation kx² + kx + 1 = −4x² – x has real and equal roots.

Answer 1

Given:

kx² + kx + 1 = −4x² – x

Bring all terms to one side:

kx² + kx + 1 + 4x² + x = 0

(k + 4)x² + (k + 1)x + 1 = 0

Here,

a = k + 4, b = k + 1, c = 1

b² − 4ac = 0

(k + 1)² − 4(k + 4) (1) = 0

k² + 2k + 1 − 4k − 16 = 0

k² − 2k − 15 = 0

(k − 5) (k + 3) = 0

k = 5 or k = −3