If 2 is a root of the quadratic equation and the quadratic equation has equal roots, find the value of k.

Question

Philoid · Accepted Answer

For a quadratic equation, ax² + bx + c = 0,

D = b² – 4ac

If D = 0, roots are equal

Given, 2 is a root of the quadratic equation

⇒ 3 × 4 + 2p – 8 = 0

⇒ 2p = -4

⇒ p = -2

Now, the quadratic equation has equal roots

⇒ 4x² + 4x + k = 0 has equal roots

⇒ D = 16 – 16k = 0

⇒ k = 1