Question

Write the quadratic equation whose roots are solution of $2x+y=7$ and $x-y=2$.

Answer 1

The equations are given as,

$2x+y=7$ (1)

And,

$x-y=2$ (2)

From equation (1) and (2),

$x=3,y=1$

Therefore the roots are 3 and 1.

The sum of the roots is $3+1=4$ and the product of the roots is $3\times 1=3$.

The quadratic equation will be of the form,

$x^2-\left(sumoftheroots\right)\times x+productoftheroots=0$

$x^2-4x+3=0$