Find the values of p for which the quadratic equation has equal roots. Also, find these roots.

Question

Philoid · Accepted Answer

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

D = b² – 4ac

If D = 0, roots are equal

⇒ D = (7p + 2)² – 4(7p – 3)(2p + 1) = 0

⇒ 49p² + 28p + 4 – 56p² + 12 – 4p = 0

⇒ 7p² – 24p – 16 = 0

⇒ 7p² – 28p + 4p – 16 = 0

⇒ 7p(p – 4) + 4(p – 4) = 0

⇒ (7p + 4)(p – 4) = 0

⇒ p = -4/7, 4