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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Updated on: 10-Oct-2022

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