Solution assignment 01 Quadratic equations (abc-formula)

Solve:

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

This equation can be solved quite easily by factorizing.
We write:

$x^2+7x+12=(x+4)(x+3)=0$

and thus the solutions are:

$x=-4$ or $x=-3$

If you want to use the $abc$ -formula we take the famous $abc$ -formula:

$x_{1,2}=\displaystyle\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

In this case:

$x_{1,2}=\displaystyle\frac{-7\pm\sqrt{7^2-4.1.12}}{2.1}=\displaystyle\frac{-7\pm1}{2}$

and thus the solutions are:

$x_1=-4$ or $x_2=-3$

which are equal to the solutions we found earlier.