Question

How do you solve $x^2-x-1=0$using the quadratic formula?

Answer 1

Simplify $x^2-x-1=0$by using quadratic formula:

Given, the equation is $x^2-x-1=0$.

It's known that the quadratic formula for $a{x}^2+bx+c=0$ is $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$.
Compare $x^2-x-1=0$with $a{x}^2+bx+c=0$,

Where $a=1,b=-1$and $c=-1.$
Substitute the above values in the above formula:
$\begin{array}{rcl}x& =& \frac{-(-1)\pm \sqrt{(-1{)}^2-4(1\left)\right(-1)}}{2·1}\\ & =& \frac{1\pm \sqrt{1+4}}{2}\\ & =& \frac{1+\sqrt{5}}{2}\mathrm{or}\frac{1-\sqrt{5}}{2}\\ & \approx & 1.62\mathrm{or}-0.62\end{array}$
Therefore, by using the quadratic formula the roots of $x^2-x-1=0$is $1.62or-0.62$.