Question

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

Answer 1

P(x) = 5x² + 5x + 1

α + β = `(-b)/a = (-5)/5` = – 1

αβ = `c/a = 1/5`

α^–1 + β^–1  = `1/α + 1/β`

= `((α + β))/(αβ)`

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

= – 5