Question

If $x=1$ is a zero of the polynomial $f\left(x\right)=x^3-2x^2+4x+k$, find the value of $k$

Answer 1

In the given polynomial $f\left(x\right)=x^3-2x^2+4x+k$, substitute $x=1$ as shown below:

$f\left(1\right)=1^3-(2\times 1^2)+(4\times 1)+k=1-2+4+k=3+k$

Therefore, $f\left(1\right)=3+k$.

Since it is given that $x=1$ is a zero of the polynomial $f\left(x\right)=x^3-2x^2+4x+k$, therefore $f\left(1\right)=0$ that is:

$3+k=0$

$\Rightarrow k=-3$

Hence $k=-3$.