Question

Find the quadratic polynomial in each case , with the given numbers as the sum and product of its zeroes respectively .
1,1

Answer 1

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