Question

If roots of the equation $x^2-7x+12=0$ are perpendicular and base length of a right angled triangle, then the length of hypotenuse of the triangle is

Answer 1

$x^2-7x+12=0$
$\Rightarrow x^2-3x-4x+12=0\Rightarrow (x-3)(x-4)=0\Rightarrow x=3,4$
So, the hypotenuse
$=\sqrt{3^2+4^2}=5$