Given quadratic equation is px (x – 2) + 6 = 0
⇒ px2 − 2px + 6 = 0 … (1)
By comparing equation (1)with ax2 + bx + c = 0,
we get a = p, b = −2p and c = 6.
Since given that the given quadratic equation has equal roots.
∴ D = b2– 4ac = 0 (∵ for equal roots D = 0)
⇒(−2p)2 − 4 × p × 6 = 0
⇒ 4p2 − 24p = 0
⇒ 4p (p – 6) = 0
⇒ p = 0 or p – 6 = 0
⇒ p = 0 or p = 6 but p ≠ 0
(∵ If p = 0 then given equation is not quadratic equation)
Hence the value of p is 6, for which the given quadratic equation have equal roots.