Question

Find the coefficient of $x^2$ in a quadratic polynomial each with the given numbers as the sum and product of its zeros respectively. $-\frac{1}{4},\frac{1}{4}$

Answer 1

Let the quadratic polynomial be $a{x}^2+bx+c$ and the zeros be $\alpha \beta$
Given that,
$\alpha +\beta =\frac{-b}{a}=\frac{-1}{4}$
$\alpha \beta =\frac{c}{a}=\frac{1}{4}$
If $a=4,b=1,c=1$
The quadratic polynomial is $4x^2+x+1$