Question

Construct a quadratic equation whose roots are $\frac{1}{4},-1$.

Answer 1

The quadratic equation whose roots are $y_4,-1$ is

$(x-y_4)(x+1)=0$

or, $x^2+(-y_4+1)x-1/4=0$

or, $x^2+\frac{3x}{4}-1/4=0$

or, $4x^2+3x-1=0$.