Question

if alpha and beta are the zeros of the polynomial x square - 5 x + K such that Alpha subtract beta equal to 1 find the value of k.

Answer 1

$zeros \: are \: \: \: \alpha \: and \: \beta \\ p(x) = {x}^{2} - 5x + k \\ \alpha - \beta = 1 \\ comparing \: eq. \: with \\ a {x}^{2} + bx + c \\ a = 1 \\ b = - 5 \\ c = k \\ \alpha + \beta = \frac{ - b}{a} \\ \alpha + \beta = 5 \\ \\ \alpha - \beta = 1 \\ \alpha + \beta = 5 \\ subtracting \: both \\ 2 \alpha = 6 \\ \alpha = 3 \\ so \: \beta = 2 \\ \alpha \beta = \frac{c}{a } \\ 2 \times 3 = k \\ k = 6$