Find a cubic polynomial whose zeros are 3, 5 and −2.

Let $\alpha, \beta$ and $\gamma$ be the zeroes of the required polynomial.

Then we have :

$\alpha+\beta+\gamma=3+5+(-2)=6$

$\alpha \beta+\beta \gamma+\gamma \alpha=3 \times 5+5 \times(-2)+(-2) \times 3=-1$

and $\alpha \beta \gamma=3 \times 5 \times-2=-30$

Now, $p(x)=x^{3}-x^{2}(\alpha+\beta+\gamma)+x(\alpha \beta+\beta \gamma+\gamma \alpha)-\alpha \beta \gamma$

$=x^{3}-x^{2} \times 6+x \times(-1)-(-30)$

$=x^{3}-6 x^{2}-x+30$

So, the required polyn omial is $p(x)=x^{3}-6 x^{2}-x+30$.