Write the family of quadratic polynomials having

We know that, if $x=\alpha$ is a zero of a polynomial then $x-2$ is a factor of quadratic polynomials.

Since $\frac{-1}{4}$ and 1 are zeros of polynomial.

Therefore $\left(x+\frac{1}{4}\right)(x-1)$

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

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

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

$=x^{2}-\frac{3}{4} x-\frac{1}{4}$

Hence, the family of quadratic polynomials is $f(x)=k\left(x^{2}-\frac{3}{4} x-\frac{1}{4}\right)$, where $k$ is any non-zero real number