Question

6. Find the value of k for which the quadratic equation (k - 12)x² + 2(k - 12)x+ 2 = 0 has two
real equal roots.​

Answer 1

Answer:ere, a = k – 12, b = 2 (k – 12), c = 2

∴ D = b2 – 4ac = [2(k– 12)]2

– 4(k – 12) x 2

= 4 (k – 12)2 – 8 (k– 12)

Roots are equal, if D = 0

⇒ 4 (k – 12) 2 – 8 (k – 12) = 0

⇒ 4(k – 12)(k – 12 – 2) = 0

⇒ (k – 12) (k – 14) = 0

⇒ k = 12 or 14

But k = 12 does not satisfy the eqn.

k = 14 Ans.