Question

Find the value of P such that the difference of the roots of the equation x² – Px + 8 = 0 is 2.

Answer 1

Let α, β be the roots of the equation x² – Px + 8 = 0

Therefore α + β = P and α . β = 8.

Now `"a" - beta = +- sqrt((alpha + beta)^2 - 4alphabeta)`

Therefore 2 = `+- sqrt("P"^2 - 32)`

⇒ P² – 32 = 4

i.e., P = ± 6