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