Find the polynomial, if the sum and the product of whose zeros are $-3$ and $2$ respectively.
Given :
The sum and the product of zeros of the polynomial are $-3$ and $2$.
To do :
We have to find the polynomial.
Solution :
Let $\alpha$ and $\beta$ are the roots of the required polynomial.
So, $\alpha + \beta = -3$
$\alpha \times \beta = 2$
If $\alpha$ and $\beta$ are the roots of the polynomial, then the polynomial is,
$x^2 -(\alpha + \beta)x + ( \alpha \times \beta) = 0$
$x^2 - (-3)x + 2= 0$
$x^2 +3x + 2 = 0$
Therefore, the required polynomial is $x^2 +3x +2=0$.
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