Question

Using graph $y=x^2$, solve the equation $x^2-x-6=0$.

Answer 1

Solution:

The roots of the equation $x^2-x-6=0$ are the x-co-ordinates of the points of the intersection of the parabola $y^2=x$ and the straight line $y=x+6.$

Consider $y=x^2$

$x$	$-3$	$-2$	$-1$	$0$	$1$	$2$	$3$
$y$	$9$	$4$	$1$	$0$	$1$	$4$	$9$

Consider $y=x+6$

$x$	$-3$	$-2$	$-1$	$0$	$1$	$2$	$3$
$y$	$3$	$4$	$5$	$6$	$7$	$8$	$9$

Hence, the solution set is $\{-2,3\}.$