Question

Find a quadratic polynomial, the sum and product of whose zeroes are $\frac{1}{4},-1$ respectively

Answer 1

Given, Sum of zeros $=\frac{1}{4}$

and Product of zeros $=-1$

Hence, quadratic polynomial is given by

$p\left(x\right)=x^2-$ (sum of zeros)$x+$ product of zeros

$\Rightarrow p\left(x\right)=x^2-\frac{1}{4}x-1\Rightarrow p\left(x\right)=\frac{1}{4}(4x^2-x-4)$