Question

A quadratic equation whose one root is $2$ and the sum of whose roots is $280$ is .

Answer 1

Let $\alpha$ and $\beta$ be the roots of the quadratic equation.

Given:Sum of the roots$=\alpha +\beta =280$

And one root is $2$

$\Rightarrow \alpha =2$

$\Rightarrow \beta =280-2=278$

$\therefore$ the quadratic equation is $x^2-(\alpha +\beta )x+\alpha \beta =0$

or $x^2-280x+2\times 278=0$

or $x^2-280x+556‬=0$ is the required quadratic equation.