Question

$\alpha$ is a root of the equation: $x^2-5x+6=0$ and $\beta$ is a root of the equation $x^2-x-30=0,$ then coordinates $(\alpha ,\beta )$ of the point P farthest from the origin are

• A. $(2,6)$
• B. $(2,3)$
• C. $(6,-5)$
• D. $(3,6)$

Answer 1

The correct option is D $(3,6)$

$x^2-5x+6=0$
$(x-3)(x-2)=0$
$\therefore \alpha$ can be $3$ or $2.$
$x^2-x-30=0$
$(x-6)(x+5)=0$
$\therefore \beta$ can be $6$ or $-5.$
So points which is farthest from origin is $(3,6).$