Question

If alpha and beta are 0s of polynomials f {x} = x square - 6x + k find value of k alpha square + beta square = 40

Answer 1

given that a
$\alpha ^{2} + \beta {}^{2} = 40$
but
$\alpha + \beta = - b \div a \\ sqare \: the \: both \: side \: w \: obtaain \: that \\ \alpha {}^{2} + \beta {}^{2} + 2 \alpha \beta = ( - 6 ) {}^{2} \\ therefore \: 40 + 2 \alpha \beta = 36 \\ 2 \alpha \beta = 36 - 40 = - 4 \\ \alpha \beta = - 4 |2 = - 2 \\ therefore \: c |a = - 2 \\ now \: c = - 2$