Question

If alpha and beta r the zeroes of the polynomial f (x) =x^2-5x+k such that aplha minus beta is one find k

Answer 1

From the polynomial
$\alpha + \beta = 5 \\ \alpha \beta = k$
Given
$\alpha - \beta = 1$
Using the identity,
${( \alpha + \beta )}^{2} - {( \alpha - \beta )}^{2} = 4 \alpha \beta \\ {5}^{2} - {1}^{2} = 4 \times k \\ k = \frac{24}{4} = 6$