Question

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

Answer 1

Let the zeroes of the polynomial be, $a$ and $b$. Then,

$a+b=\frac{1}{4}$

$ab=-1$

General quadratic equation with roots $a,b$ is,

$x^2-(a+b)x+ab=0$

$\Rightarrow x^2-\frac{x}{4}-1=0$

$\Rightarrow 4x^2-x-4=0$

Hence, $4x^2-x-4=0$ is the required quadratic polynomial.