Question

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

Answer 1

We have,

$-b/a=1/4\Rightarrow b/a=-1/4$

$c/a=-1$

Since,

${ax}^2+bx+c=0$ be a polynomial.

$x^2+\frac{b}{a}x+\frac{c}{a}=0\Rightarrow x^2-\frac{1}{4}x-1=0$

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

Hence, this is the answer.