Question

Solve $x^2-7x+12=0$ by Formula Method.

Answer 1

Given :

$x^2-7x+12=0$

The given equation is in the form of $a^2-bx+c=0$

where $a=1,b=-7,c=12$

The quadratic formula is,

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Now, by substituting the values, we get:

$$\begin{gathered} \Rightarrow x=\frac{7\pm \sqrt{49-48}}{2} \\ \Rightarrow x=\frac{7\pm \sqrt{1}}{2} \\ \Rightarrow x=\frac{7\pm 1}{2} \end{gathered}$$

If $x=\frac{7+1}{2}=\frac{8}{2}=4$.

If $x=\frac{7-1}{2}=\frac{6}{2}=3$.

Therefore, $4$ and $3$ are the roots of the given equation $x^2-7x+12=0$