Question

The roots of x2 - 4x = 5, in ascending order, are ? and ?

Answer 1

For finding the roots of the function, we have to writte the equation in this form:

$ax^2+bx+c=0$

So in our problem will be:

$x^2+(-4)x-5=0$

Now we can use the cuadratic equation that is:

$\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$

and in our problem will be:

$\begin{gathered} \frac{4\pm\sqrt[]{16^{}-4(1)(-5)}}{2(1)} \\ \frac{4\pm\sqrt[]{16^{}+20}}{2} \\ \frac{4\pm\sqrt[]{36}}{2} \\ \frac{4\pm6}{2} \end{gathered}$

Now we can find our two solutions or roots, one with the + and the other with the -

1)

$\begin{gathered} x=\frac{4+6}{2} \\ x=\frac{10}{2} \\ x=5 \end{gathered}$

2)

$\begin{gathered} x=\frac{4-6}{2} \\ x=\frac{-2}{2} \\ x=-1 \end{gathered}$

so the roots are going to be: -1, 5