Find the value of "p", if the quadratic equation p ²x ²â€“12x + p + 7 = 0 has the root .

p ² x ² – 12x + p + 7 = 0,

a = p ² ,

b = -12,

c = p + 7.

,

let the other root be α .

-------- (1)

∴

-----------(2)

Comparing (1) and (2)

3(24 – 3p ² ) = 4p + 28
72 – 9p ² = 4p + 28
Thus we get 9p ² + 4p – 44 = 0
Now by applying the formula:

In this problem, a = 9, b = 4, c = -44

∴ The value of p is 2 or