Question

Find the quadratic polynomial whose zeros are given as following
$\frac{1}{4},-1$

Answer 1

Let the quadratic polynomial be
$a{x}^2+bx+c\ne 0$
and its zeroes be
$\alpha =\frac{1}{4}$ and $\beta =-1$
Sum of the zeroes $=\alpha +\beta$
$\frac{1}{4}+(-1)=\frac{1-4}{4}=\frac{-3}{4}$
Product of the zero $=\alpha \beta =\frac{1}{4}\times -1=-\frac{1}{4}$
The quadratic polynomial will be
$a{x}^2+bx+c$ is ,
$k[x^2-(\alpha +\beta )x+\left(\alpha \beta \right)]$
$k[x^2-(-\frac{3}{4})x+(-\frac{1}{4})]$
If K = 4,the qudratic polynomial will be
$4[x^2+\frac{3}{4}x-\frac{1}{4}]$
$\Rightarrow 4x^2+3x-1$