Question

If x-2 is a factor of the polynomial 2x²+kx+15 then the value of k is​

Answer 1

Answer:

k=-11.5

Step-by-step explanation:

x-2 = 0

x = 2

2x^2+kx+15=0

2×(2)^2+k×2+15=0

2×4+k×2+15=0

8+k×2+15=0

k×2=-8-15

k=-23/2

k=-11.5

Answer 2

$\sf \Large Solution!!$

$\sf \large Given:$

$\sf \to 2x^{2}+kx+15$

$\sf \to (x-2)\:is\:a\:factor\:of\:the\:above\:polynomial$

$\sf \large So,$

$\sf \to x-2=0$

$\sf \to x=2$

$\sf \large Now,$

$\sf \to f(x)=2x^{2}+kx+15$

$\sf \to f(2)=2(2)^{2}+k(2)+15$

$\sf Since\:(x-2)\:is\:a\:factor,$

$\sf \to 0=8+2k+15$

$\sf \to 0=23+2k$

$\sf \to -23=2k$

$\sf \to \dfrac{-23}{2}=k$

$\sf \boxed{\bigstar k=-11.5\:or\:-11\dfrac{1}{2}}$