Question

If alpha and beta are zeroes of y²-5y+m,find the value of m such that (alpha-beta)²-alpha * beta =24

Answer 1

$\alpha + \beta = 5 \\ \alpha \beta = m \\ {( \alpha - \beta) }^{2} = {( \alpha + \beta )}^{2} - 4 \alpha \beta = {5}^{2} - 4m = 25 - 4m \\ {( \alpha - \beta )}^{2} - \alpha \beta = 25 - 4m - m = 25 - 5m = 24 \\ 5m = 1 \\ m = \frac{1}{5} = 0.2$