Question

If α, β are zeroes of quadratic polynomial 5x² + 5x + 1, find the value of α² + β².

Answer 1

P(x) = 5x² + 5x + 1

α + β = `(-b)/a = (-5)/5` = – 1

αβ = `c/a = 1/5`

α² + β² = (α + β)² – 2αβ

= `(-1)^2 - 2(1/5)`

= `1 - 2/5`

= `3/5`