Question

write the quadratic eq. which has the product of two root is 5 an the sum is 2 root 5​

Answer 1

Let the zeros if the quadratic equation be \alpha and \beta

$\alpha \beta = 5$

$\alpha + \beta = 2 \sqrt{5}$

We know that, for any quadratic equation

$k(x {}^{2} + ( \alpha + \beta )x + \alpha \beta )$

$= > k(x {}^{2} + 2 \sqrt{5} x + 5)$

This the quadratic equation whose sum of the zeros us 2√5 and product is 5