Question:
Verify that:
(i) 4 is a zero of the polynomial $p(x)=x-4$.
(ii) $-3$ is a zero of the polynomial $q(x)=x+3$.
(iii) $\frac{2}{5}$ is a zero of the polynomial, $f(x)=2-5 x$.
(iv) $\frac{-1}{2}$ is a zero of the polynomial $g(y)=2 y+1$.
Solution:
(i) $p(x)=x-4$
$\Rightarrow p(4)=4-4$
= 0
Hence, 4 is the zero of the given polynomial.
(ii) $p(x)=(-3)+3$
$\Rightarrow p(3)=0$
Hence, 3 is the zero of the given polynomial.
(iii) $p(x)=2-5 x$
$\Rightarrow p\left(\frac{2}{5}\right)=2-5 \times\left(\frac{2}{5}\right)$
$=2-2$
$=0$
Hence, $\frac{2}{5}$ is the zero of the given polynomial.
(iv) $p(y)=2 y+1$
$\Rightarrow p\left(-\frac{1}{2}\right)=2 \times\left(-\frac{1}{2}\right)+1$
$=-1+1$
$=0$
Hence, $-\frac{1}{2}$ is the zero of the given polynomial.