The value of ' p ' for which the equation x 2 + p x y + y 2 - 5 x - 7 y + 6 = 0 represents a pair of straight lines, is

Step-by-step solution

Given equation x 2 + p x y + y 2 - 5 x - 7 y + 6 = 0 Will represent a pair of straight lines, if ∆ = 0 ⇒ 1 ⋅ 1 ⋅ 6 + 2 - 7 2 - 5 2 p 2 - 1 - 7 2 2 - 1 - 5 2 2 - 6 p 2 2 = 0 ⇒   6 + 35 p 4 - 49 4 - 25 4 - 6 p 2 4 = 0 ⇒   35 p - 50 - 6 p 2 = 0 ⇒   2 p - 5 3 p - 10 = 0 ⇒   p = 5 2 , 10 3