Verify whether the following is zeroes of the polynomial, indicated against them.
$p (x) = 3 x + 1, x = - \frac{1}{3}$

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Solution

If $x = - \frac{1}{3}$ is zeroes of the polynomial then $p (x) = 0$

We have, $p (x) = 3 x + 1$
$p (- \frac{1}{3}) = (3 \times - \frac{1}{3}) + 1$
$= - 1 + 1$
$= 0$
$∴ p (- \frac{1}{3}) = 0$

So, $x = - \frac{1}{3}$ is the zeroes of the polynomial $p (x)$ .

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Verify whether the following is zeroes of the polynomial, indicated against them.p(x)=3x+1,x=−13

If x=−13 is zeroes of the polynomial then p(x)=0We have, p(x)=3x+1p(−13)=(3×−13)+1=−1+1=0∴p(−13)=0So, x=−13 is the zeroes of the polynomial p(x).

Verify whether the following is zeroes of the polynomial, indicated against them.
$p (x) = 3 x + 1, x = - \frac{1}{3}$

If $x = - \frac{1}{3}$ is zeroes of the polynomial then $p (x) = 0$

We have, $p (x) = 3 x + 1$
$p (- \frac{1}{3}) = (3 \times - \frac{1}{3}) + 1$
$= - 1 + 1$
$= 0$
$∴ p (- \frac{1}{3}) = 0$

So, $x = - \frac{1}{3}$ is the zeroes of the polynomial $p (x)$ .