Question

For what value of k is-2azero of the polynomial x2-x(2k+2)

Answer 1

$</p><p>{\huge{\red{\boxed{\mathbb{\blue{\underline{\blue{A}{\red{N}{\pink{S}{\orange{W}{\red{E}{\purple{R} }}}}}}}}}}}}$

$p(x) = x^{2} - x (2k + 2)$

if -2 is a zero of $p(x)$ , then

$p( - 2) = 0 \\ = > p( - 2) = ( - 2)^{2} - 2(2k + 2) \\ = > 4 - 2(2k + 2) \\ = > 2(2k + 2) \\ = > 4k + 4$

-2 is a zero of $p(x)$ so,

$4k + 4 = 0 \\ = > 4k = - 4 \\ = > k = \frac{ - 4}{4} \\ = > k = - 1$

Hence the value of k is -1