Question

If α, β are the zeros of the polynomial f(x) = x² – 5x + k such that α – β = 1, find the value of k.

Answer 1

Given: Let α, β be zeros of f(x) = x² – 5x + k and α – β = 1.

For a quadratic x² + bx + c, α + β = –b and αβ = c. 

Here α + β = 5 and αβ = k.

(α – β)² = 1 

⇒ (α + β)² – 4αβ = 1 

⇒ 5² – 4k = 1

⇒ 25 – 4k = 1

⇒ 4k = 24

⇒ k = 6