Question:
If $x=1$ is a zero of the polynomial $f(x)=x^{3}-2 x^{2}+4 x+k$, write the value of $k$.
Solution:
We have to find the value of $K$ if $x=1$ is a zero of the polynomial $f(x)=x^{3}-2 x^{2}+4 x+k$.
$f(x)=x^{3}-2 x^{2}+4 x+k$
$f(1)=1^{3}-2(1)^{2}+4 \times 1+k$
$0=1-2+4+k$
$0=5-2+k$
$0=3+k$
$-3=k$
Hence, the value of $k$ is $k=-3$