Question

if alpha , beta are zeroes of the polynomial p(x)=kx²+x-6 such that alpha²+beta²=25/4,find the value of k

Answer 1

${ \alpha }^{2} + { \beta }^{2} = \frac{25}{4} \\ ( { \alpha + \beta )}^{2} - 2 \alpha \beta = \frac{25}{4} \\ ( - \frac{1}{k} ) {}^{2} - 2 \frac{6}{k} \: = \frac{25}{4}$

Answer 2

See the attachment for detail solution
Hope this will help you