Question

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

Answer 1

Given,

Sum of roots $=\frac{1}{4}$

Product of roots $=-1$

$P\left(x\right)=x^2-(sum-of-roots)x+(product-of-roots)$

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

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

is the required differential equation.