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Question:

Write a quadratic polynomial, sum of whose zeros is $2 \sqrt{3}$ and their product is 2 .

Solution:

Let $S$ and $P$ denotes respectively the sum and product of the zeros of a polynomial are $2 \sqrt{3}$ and 2 .

The required polynomial $g(x)$ is given by

$g(x)=k\left(x^{2}-S x+P\right)$

$g(x)=k\left(x^{2}-2 \sqrt{3} x+2\right)$

Hence, the quadratic polynomial is $g(x)=k\left(x^{2}-2 \sqrt{3} x+2\right)$ where $k$ is any non-zeros real number.