Question

Solve the quadratic equation $x^2-x-2=0$ graphically.

Answer 1

This second degree equation will give a parabola once plotted on the paper.

The solution of the equation are the points corresponding to $y=0$ and $y=x^2-x-2$.

We simplify the 2nd eqn to find the vertex of the parabola.

$y=x^2-x-2$

$⟹y=x^2-x+\frac{1}{4}-\frac{1}{4}-2$

$⟹y=(x-\frac{1}{2}{)}^2-\frac{9}{4}$

$(y+\frac{9}{4})=(x-\frac{1}{2}{)}^2$

This tells us that Parabola's mouth is towards positive y-axis with vertex at

$(\frac{1}{2},\frac{-9}{4})$

Its intersection with line $y=0$ is at points $(2,0)$ and $(-1,0)$.

So, the solutions are $x=2$ and $x=-1$