Question

Find the value of ‘K’ for which x = 3 is a solution of the quadratic equation, (K + 2)x² – Kx + 6 = 0. Also, find the other root of the equation.

Answer 1

(K + 2)x² – Kx + 6 = 0 …(1)
Substitute x = 3 in equation (1)
(–4 + 2)x² –(–4)x + 6 = 0
⇒ –2x² + 4x + 6 = 0
⇒ x² – 2x – 3 = 0    ...(Dividing by 2)
⇒ x² – 3x + x – 3 = 0
⇒ x(x – 3) + 1(x – 3) = 0
(x + 1)(x – 3) = 0
So, the roots are x = –1 and x = 3
Thus, the other root of the equation is x = –1.