Question

Discuss the nature of the roots
x² + 2(k+2)+9k=0, find the value of k​

Answer 1

On comparing x² + 2(k+2)x+9k=0 with standard form ax²+bx+c = 0, we get

a = 1, b = 2(k+ 2) and c = 9k

For, x² + 2(k+ 2)x+9k = 0, value of discriminant,

D = 6²-4ac

⇒ D = 4(k+ 2)²-4(9k)

The roots of quadratic equation are real and equal only when discriminant, D = 0.

⇒ 4(k+ 2)²−4(9k) = 0

⇒ (k+ 2)² = 9k

⇒ k² 5k + 4 = 0

⇒ k² − 4k − k + 4 = 0 -

⇒ k² − k − 4k+ 4 = 0 -

⇒ k(k − 1) − 4(k − 1) = 0 -

⇒ (k − 4) (k − 1) = 0