Question

Solve the following quadratic equation.

`1/(4 - "p") - 1/(2 + "p") = 1/4`

Answer 1

`1/(4 - "p") - 1/(2 + "p") = 1/4`

∴ `(2 + "p" - (4 - "p"))/((4 - "p")(2 + "p")) = 1/4`

∴ `(2 + "p" - 4 + "p")/(8 + 4"p" - 2"p" - "p"^2) = 1/4`

∴ `(2"p" - 2)/(8 + 2"p" - "p"^2) = 1/4`

∴ 4(2p – 2) = 8 + 2p – p²

∴ 8p – 8 = 8 + 2p – p²

∴ p² – 2p + 8p – 8 – 8 = 0

∴ p² + 6p – 16 = 0

-16

8  -2

8 × (-2) = -16

8 - 2 = 6

∴ p² + 8p – 2p – 16 = 0

∴ p(p + 8) – 2(p + 8) = 0

∴ (p + 8)(p – 2) = 0

By using the property, if the product of two numbers is zero, then at least one of them is zero, we get

p + 8 = 0 or p – 2 = 0

∴ p = – 8 or p = 2

∴ The roots of the given equation are – 8 and 2.