Question

For what value of $k$, is $3$ a zero of the polynomials $2x^2+x+k$

Answer 1

Given $p\left(x\right)=2x^2+x+k$

$x=3$

Put $x=3$

$\Rightarrow$$p\left(3\right)=2(3{)}^2+(3)+k$

$\Rightarrow$$2(3{)}^2+(3)+k=0$

$\Rightarrow$$2.9+3+k=0$

$\Rightarrow$$18+3+k=0$

$\Rightarrow$$21+k=0$

$\Rightarrow$$k=-21$