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} \\ (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=(4+6)/(2) \\ x=(10)/(2) \\ x=5 \end{gathered}`

2)

`\begin{gathered} x=(4-6)/(2) \\ x=(-2)/(2) \\ x=-1 \end{gathered}`

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