Question

If α,β are the zeros of the quadratic polynomial x^2+kx+12 such that α-β=1, find the value of k

Answer 1

$heya \\ \\ ( \alpha - \beta ) = \sqrt{( \alpha + \beta ) {}^{2} - 4 \alpha \beta } \\ \\ ( \alpha + \beta ) = - k \\ and \\ ( \alpha \beta ) = 12 \\ \\ \\ \\ k {}^{2} - 48 = + 1 \\ \\ or \\ \\ k = 7 \: \: \: \: \: or \: \: \: \: \: \: k = - 7$