Question

one of the zeros of quadratic polynomial 4 x square - 8k x minus 9 is equal in magnitude but opposite in sign of the Other find the value of k

Answer 1

since
$\alpha = - \beta \\ hence \: \alpha + \beta = 0........1 \\ and \: we \: know \: that \: sum \: of \: \\ zeroes \: of \: quadratic \: polynomia \\ is \: (\alpha + \beta ) = \: \frac{ - b}{a} ........2 \: where \: a \: and \: b \: are \: \\ coefficient \: of \: {x}^{2} \: and \: x \: respectively \\ \\ and \: product \: of \: zeroes \: \: is \: given \\ as (\: \alpha \times \beta ) \: = \frac{c}{a} \: where \: c \: is \: cnstant \\ then from \: 1 \: and \: 2 \: we \: have \\ \frac{ - b}{a} = 0 \: i.e \frac{ - ( - 8k)}{4} = 0 \\ 8k = 0 \\ k = 0$