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