Question

plzz tell me question 8 and 9 fast

Answer 1

ANS:-8

let the given polynomial be
$f(x) = {kx}^{2} + 4x + 4$
if
$\alpha \: and \: \beta$
are the zeroes of the polynomial f(x).
$\alpha + \beta = - \frac{4}{k} ............(1) \\ \alpha \beta = \frac{4}{k } ............(2)$
the given condition is:
${ \alpha + \beta }^{2} - 2 \alpha \beta = 24 \\ multiplying \: the \: whole \: equation \: \: \: by \: {k}^{2}$
${24k}^{2} + 8k - 16 = 0 \\ {3k}^{2} + k - 2 = 0 \\ {3k}^{2} + 3k - 2k - 2 = 0 \\ 3k(k + 1) - 2(k + 1) = 0 \\ (k + 1)(3k - 2) = 0 \\ therefore \: \\ k + 1 = 0 \: or \: 3k - 2 = 0 \\ \\ i.e \\ k = - 1 \: or \: k = \frac{2}{3}$
hope it's helps you