Question

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

Answer 1

Sum of zeroes $=2\sqrt{3},$ Product $=2$

$\Rightarrow$ Using, sum of zeroes $=-$ coefficient of term $x.$

$\Rightarrow$ Product of zeroes $=$ coefficient of constant term.

$\Rightarrow$ Quadratic polynomial can be $=x^2-2\sqrt{3}x+2.$

Hence, the answer is $x^2-2\sqrt{3}x+2.$