Question

if one of the zeroes of the quadratic polynomial f(x)= 14x2-42k2x-9 is negative of the other , then find value of k

Answer 1

we know that
$\alpha + \beta = \frac{ - b}{a} \\ here \: one \: zero \: is \: \: negative \: of \: other \\ let \: one \: zero \: is \: \alpha \: and \: other \: will \: be \: - \alpha . \\ so \: sum \: of \: zeros \\ \alpha - \alpha = \frac{ - b}{a} \\ 0 = \frac{42 {k}^{2} }{14} \\ 42 {k}^{2} = 0 \\ {k}^{2} = 0 \\ k = 0$