Question

Find the coefficient of $x$ in a quadratic polynomial each with the given numbers as the sum and product of its zeros respectively. $0,\sqrt{5}$

Answer 1

Let the quadratic polynomial be $a{x}^2+bx+c$ and the zeros be $\alpha \beta$
Given that,
$\alpha +\beta =\frac{-b}{a}=0$
$\alpha \beta =\frac{c}{a}=\sqrt{5}$
The quadratic polynomial is $x^2+\sqrt{5}$