For what value of k, are the roots of the quadratic equation (k – 12) x2 + 2 (k – 12) x + 2 = 0 equal?

Question

Philoid · Accepted Answer

For equal roots, the value of discriminant should be zero i.e.,

D = b² – 4ac

⇒ D = (2k – 24)² – 4(k – 12) (2) = 0

⇒ 4k² – 96k + 576 – 8k + 96 = 0

⇒ 4k² – 104k + 672 = 0

⇒ k² – 26k + 168 = 0

⇒ k² – 14k – 12k + 168 = 0

⇒ k (k – 14) – 12(k – 14) = 0

⇒ (k – 14) (k – 12) = 0

⇒ k – 14 = 0 and k – 12 = 0

⸫ k = 14 and k = 12

For what value of k, are the roots of the quadratic equation (k – 12) x² + 2 (k – 12) x + 2 = 0 equal?