Question

If α, β are zeroes of the polynomial p(x) = 5x² – 6x + 1, then find the value of α + β + αβ.

Answer 1

Given: Let α, β be the zeros of p(x) = 5x² – 6x + 1.

For a quadratic `ax^2 + bx + c, α + β = -b/a` and `αβ = c/a`.

`α + β = -(-6)/5 = 6/5`.

`αβ = 1/5`.

`α + β + αβ = 6/5 + 1/5 = 7/5`.