Question

If $x=-\frac{1}{3}$ is a zero of a polynomial $p\left(x\right)=27x^3-{ax}^2-x+3$, then find the value of ${}^{\prime }{a}^{\prime }$

Answer 1

$x=-\frac{1}{3}$ is a zero of polynomial $p\left(x\right)$

$⟹p(-\frac{1}{3})=0$

$⟹27(-\frac{1}{3}{)}^3-a(-\frac{1}{3}{)}^2-(-\frac{1}{3})+3=0$

$⟹-\frac{27}{27}-\frac{a}{9}+\frac{1}{3}+3=0$

$⟹\frac{a}{9}=2+\frac{1}{3}$

$⟹\frac{a}{9}=\frac{7}{3}$

$⟹a=21$