Question

If x-2 is a factor of 2 x^2 +5x+k then the
value of K is​

Answer 1

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

GIVEN

$\: \sf{ \: x - 2 \: \:is \: a \: factor \: of \: }2 {x}^{2} + 5x + k$

TO DETERMINE

The value of k

EVALUATION

Let

$f(x) = x - 2$

$g(x) = 2 {x}^{2} + 5x + k$

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

$f(x) = 0$

$\implies \: x - 2 = 0$

$\implies \: x = 2$

So by the Remainder Theorem the required Remainder is

$g(2) = 2 \times {(2)}^{2} +( 5 \times 2 )+ k = k + 18$

By the given condition

$k + 18 = 0$

$\implies \: k = - 18$

RESULT

THE REQUIRED VALUE IS

$\boxed{ \: k = - 18 \: }$