Question

Find the quadratic polynomial in each case , with the given numbers as the sum and product of its zeroes respectively .
$\frac{1}{4},\frac{1}{4}$

Answer 1

Sum of the zeroes $(\alpha +\beta )=\frac{1}{4}$
Product of the zeroes $=\alpha \beta =\frac{1}{4}$
Let the Quadratic polynomial be
$a{x}^2+bx+cis$
$k[x^2-(\alpha +\beta )x+\alpha \beta ],$
where k is a constant and $k\ne 0,then$
$k[x^2-(\frac{1}{4}x+\left(\frac{1}{4}\right))]$
$\Rightarrow 4x^2-x+1$