Question

Solve graphically $2x^2+x-6=0$

Answer 1

First, let us form the following table by assigning integer values for $x$ from $-3$ to $3$ and finding the corresponding values of $y=2x^2+x-6$.

$x$	$-3$	$-2$	$-1$	$0$	$1$	$2$	$3$
$x^2$	$9$	$4$	$1$	$0$	$1$	$4$	$9$
$2x^2$	$18$	$8$	$2$	$0$	$2$	$8$	$18$
$x$	$-3$	$-2$	$-1$	$0$	$1$	$2$	$3$
$-6$	$-6$	$-6$	$-6$	$-6$	$-6$	$-6$	$-6$
$y$	$9$	$0$	$-5$	$-6$	$-3$	$4$	$15$

Plot the points $(-3,9),(-2,0),(-1,-5),(0,-6),(1,-3),(2,4)$ and $(3,15)$ on the graph.
Join the points by a smooth curve. The curve, thus obtained, is the graph of $t=2x^2+x-6$.
The curve cuts the x-axis at the points $(-2,0)$ and $(1.5,0)$
The x-coordinates of the above points are $-2$ and $1.5$
Hence, the solution set is $\{-2,1.5\}$