Question

find tha quadratic equation,if one of the roots is root5-root3
​

Answer 1

$\textbf{Given:}$

$\text{One root is \sqrt{5}-\sqrt{3} }$

$\text{Then, the other root is }\;\sqrt{5}+\sqrt{3}$

$\text{Sum of the roots =}\sqrt{5}-\sqrt{3}+\sqrt{5}+\sqrt{3}=2\sqrt{5}$

$\text{Product of the roots =}(\sqrt{5}-\sqrt{3})(\sqrt{5}+\sqrt{3})$

$\text{Product of the roots =}\sqrt{5}^2-\sqrt{3}^2=5-3=2$

$\text{The required quadratic equation is }$

$x^2-(\text{sum of the roots})x+(\text{product of the roots})=0$

$\bf\;x^2-2\sqrt{5}x+2=0$