Verify whether the given statement is true or false:
$- 3$ is the zero of $y^{2} + y - 6$ .

True

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False

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Solution

The correct option is A True
Verifying $- 3$ is the zero of $y^{2} + y - 6$ or not:
Let $p (y) =$ $y^{2} + y - 6$ .
In general, we can say that a zero of a polynomial $p (y)$ is a number $c$ , such that $p (c) = 0$ .
Therefore, if $- 3$ is the zero of $p (y)$ , then $p (- 3) = 0$
$\begin{array}{rcl} p (y) & = & y^{2} + y - 6 \\ \Rightarrow & p (- 3) = {(- 3)}^{2} + (- 3) - 6 \\ = & 9 - 3 - 6 \\ = & 9 - 9 \\ = & 0 \end{array}$
Therefore, $- 3$ is the zero of $y^{2} + y - 6$ .
Hence, the given statement is True.

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