Question

For what values of k, the roots of the quadratic equation (k + 4) x² + (k + 1) x + 1 = 0 are equal ?

Answer 1

The given quadratic equation is (k + 4)x² + (k + 1)x + 1 = 0.

For equal roots, its discriminant, D is 0.

⇒ b² − 4ac = 0 where a = k + 4, b = k + 1, c = 1

⇒ (k + 1)² − 4(k + 4) × 1 = 0

⇒ k² + 2k + 1− 4k − 16 = 0

⇒ k² − 2k − 15 = 0

⇒ k² − 5k + 3k − 15 = 0

⇒ k(k − 5) + 3(k − 5) = 0

⇒ (k − 5) (k + 3) = 0

⇒ k = 5 or k = −3

Thus, for k = 5 or k = −3, the given quadratic equation has equal roots.