Question

If x=-1/2 is a zero of polynomial p(x)=3x^3-2x^2+kx-1 then find the value of k

Answer 1

Hope it helped you.....

Answer 2

Given,

• $\sf x=\dfrac{-1}{2}$

• $\sf Polynomial=3x^3-2x^2+kx-1$

We have to find the value of k.

$\sf 3x^3-2x^2+kx-1=0$

Applying the value of x to the equation,

$\sf [3\times(\dfrac{-1}{2})^3]-[2\times(\dfrac{-1}{2})^2]+[k\times\dfrac{-1}{2}]-1=0$

$\implies \sf [3\times \dfrac{-1}{8}]-[2\times\dfrac{1}{4}]+[k\times\dfrac{-1}{2}]-1=0$

$\implies \sf \dfrac{-3}{8}-\dfrac{1}{2}-\dfrac{k}{2}-1=0$

Multiplying each term with -2,

$\implies \sf \dfrac{3}{4}+1+k+2=0$

$\implies \sf \dfrac{3}{4}+3+k=0$

$\implies \sf k=-3-\dfrac{3}{4}$

$\implies \sf k=\dfrac{-15}{4}$

$\huge\boxed{\bold{\sf{Value\:of\:k=\dfrac{-15}{4}}}}$