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### Difficult Problems

1

$x^2+6x+8=0$
2

To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where in this case $a=1$, $b=6$ and $c=8$. Then substitute the values of the coefficients of the equation in the quadratic formula:

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

$x=\frac{-6\pm 2}{2}$
3

To obtain the two solutions, divide the equation in two equations, one when $\pm$ is positive ($+$), and another when $\pm$ is negative ($-$)

$x=-2,\:x=-4$
4

Solve the equation ($1$)

$x=-2$
5

Solve the equation ($2$)

$x=-4$
6

The $2$ solutions of the equation are

$x=-2,\:x=-4$

$x=-2,\:x=-4$