Question

Find the value of ‘p’ for which the quadratic equation px(x – 2) + 6 = 0 has two equal real roots.

Answer 1

Given quadratic equation is

px(x – 2) + 6 = 0

⇒ px² – 2px + 6 = 0

For two equal and real roots

(Discriminant) D = 0

⇒ b² – 4ac = 0

Here, b = –2p, a = p, c = 6

∴ (–2p)² – 4 × p × 6 = 0

⇒ 4p² – 24p = 0

⇒ 4p(p – 6) = 0

⇒ p = 6