Question

If α, β are roots of the equation x² + px – q = 0 and γ, δ are roots of x² + px + r = 0, then the value of (α – y)(α – δ) is ______.

Options

• p + r

• p – r

• q – r

• q + r

Answer 1

If α, β are roots of the equation x² + px – q = 0 and γ, δ are roots of x² + px + r = 0, then the value of (α – y)(α – δ) is q + r.

Explanation:

α, β are roots of  x² + px – q = 0

⇒ α + β = –p,

αβ = –q

γ, δ are roots of x² + px + r = 0

⇒ γ + δ =  –p,

γδ = r

Therefore,

(α – γ)(α – δ) = α² – α(γ + δ) + γδ

= α² + pα + r

∵ α is root of x² + px – q = 0

⇒ α² + pα = q 

⇒ (α – y)(α – δ) = q + r