If -5 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, -5 is a root of the quadratic equation

⇒ 2 × 25 – 5p – 15 = 0

⇒ 35 = 5p

⇒ p = 7

Now, the quadratic equation has equal roots

⇒ 7x² + 7x + k = 0 has equal roots

⇒ D = 49 – 28k = 0

⇒ k = 49/28 = 7/4