Question

If one root of the quadratic equation $k{x}^2-20x+34=0$ is $5-2\sqrt{2}$, find the rational number k.

Answer 1

One root of the $k{x}^2-20x+34=0$ is $5-2\sqrt{2}$,
Then the other root will be $5+2\sqrt{2}$
Sum of roots $=10=\frac{20}{k}$
$\therefore$ the rational number $k=2$