Question

If x+1 is a factor of the polynomial 2x^ 2 +kx,then find the value of k​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

GIVEN

$\sf{ \: x + 1 \: \:is \: a \: factor \: of \: }2 {x}^{2} + kx$

TO DETERMINE

The value of k

EVALUATION

Let

$f(x) = x + 1$

$g(x) = 2 {x}^{2} +kx$

Now for the zero of polynomial f(x) we have

$f(x) = 0$

$\implies \: x + 1= 0$

$\implies \: x = - 1$

So by the Remainder Theorem the required Remainder is

$g(2) = 2 \times {( -1 )}^{2} + k \times ( - 1) = 2 - k$

By the given condition

$2 - k= 0$

$\implies \: k = 2$

RESULT

THE REQUIRED VALUE IS

$\boxed{ \: k = 2 \: }$