Chapter 4, Problem 12AR

To determine

To solve the given equation, $x^2-7x+12=0$ by factoring or quadratic formula.

Answer to Problem 12AR

  $x=4,3$

Explanation of Solution

Given:

The equation is, $x^2-7x+12=0$

Calculation:

We can solve the given equation by using quadratic formula.

That is,

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

The given equation $x^2-7x+12=0$ which is in the form of $a{x}^2+bx+c=0$ .

Where, $a=1,b=-7\text{ and c = 12}$ .

Now, Substitute the values in the formula then we get that,

  $\begin{array}{l}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ x=\frac{-\left(-7\right)\pm \sqrt{{\left(-7\right)}^2-4\left(1\right)\left(12\right)}}{2\left(1\right)}\\ x=\frac{7\pm \sqrt{49-48}}{2}\\ x=\frac{7\pm \sqrt{1}}{2}\\ x=\frac{7\pm 1}{2}\\ x=\frac{7+1}{2},\frac{7-1}{2}\\ x=4,3\end{array}$

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