Question

Solve the given equation graphically, $x^2-5x+6=0$

Answer 1

The given quadratic equation is $x^2-5x+6=0$.

Let $y=x^2-5x+6$, when we substitute different values of $x$ in the equation $y=x^2-5x+6$ then value of $y$ changes accordingly.

When $x=0$ then

$y=(0{)}^2-(5\times 0)+6=0-0+6=6$

The point is $(0,6)$

When $x=2$ then

$y=(2{)}^2-(5\times 2)+6=4-10+6=10-10=0$

The point is $(2,0)$

When $x=3$ then

$y=(3{)}^2-(5\times 3)+6=9-15+6=15-15=0$

The point is $(3,0)$

Therefore, the coordinates are $(0,6)$, $(2,0)$ and $(3,0)$ and the graph of the quadratic equation $y=x^2-5x+6$ is as shown above.

Hence, from above graph, we get that $x=2$ or $x=3$.