Question

In the following exercises, solve by using the Quadratic Formula:$p^2+7p+12=0$

Short answer

The solution of the above equation is$p=-3$and$p=-4$

Step-by-step solution

Given information

We are given a quadratic equation$p^2+7p+12=0$

Identify the values of a,b,c

On comparing with standard equation we get$a=1,b=7,c=12$

Write the quadratic formula and substitute the values in it

The quadratic formula can be given as

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

On substituting the values we get

$p=\frac{-7\pm \sqrt{49-4\left(1\right)\left(12\right)}}{2\left(1\right)}$

Simplify

On simplifying the equation we get,

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

On further simplifying we get

$$\begin{gathered} p=\frac{-7+1}{2} \\ p=\frac{-6}{2} \\ p=-3 \end{gathered}$$and$$\begin{gathered} p=\frac{-7-1}{2} \\ p=\frac{-8}{2} \\ p=-4 \end{gathered}$$

Conclusion

The solution of the quadratic equation is$p=-3$and$p=-4$