Question

Find the value of K (2x-3) is a factor of x cube +2xsquare -10x+K

Answer 1

Answer:

Step-by-step explanation:

g(x): x2 + 2x + k = 0

Given polynomial: 2x4 + x3 -14x2 + 5x + 6

Divide the polynomial by the factor

remainder is: ( 21 + 7k)x + (6 + 8k + 2k2) = 0

21 + 7k = 0 ⇒ k = -3.

Answer 2

$\sf\red{\underline{\underline{Answer:}}}$

$\sf{The \ value \ of \ k \ is \ -\frac{57}{8}}$

$\sf\orange{Given:}$

$\sf{The \ given \ polynomial \ is}$

$\sf{\implies{p(x)=x^{3}+2x^{2}-10x+k}}$

$\sf{\implies{The \ factor \ of \ polynomial \ is \ (2x-3)}}$

$\sf\pink{To \ find:}$

$\sf{The \ value \ of \ k.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{The \ given \ polynomial \ is}$

$\sf{\implies{p(x)=x^{3}+2x^{2}-10x+k}}$

$\sf{p(x)=0}$

$\sf{The \ factor \ of \ polynomial \ is \ (2x-3)}$

$\sf{\therefore{2x-3=0}}$

$\sf{\therefore{x=\frac{3}{2}}}$

$\sf{Substitute \ x=\frac{3}{2} \ in \ the \ given \ polynomial.}$

$\sf{\implies{(\frac{3}{2})^{3}+2\times(\frac{3}{2})^{2}-10\times\frac{3}{2}+k=0}}$

$\sf{\therefore{\frac{27}{8}+\frac{9}{2}-15+k=0}}$

$\sf{\therefore{\frac{27+36-120}{8}+k=0}}$

$\sf{\therefore{\frac{57}{8}+k=0}}$

$\sf{\therefore{k=-\frac{57}{8}}}$

$\sf\purple{\tt{\therefore{The \ value \ of \ k \ is \ -\frac{57}{8}}}}$