Question

Find the real solutions of the quadratic equation $0=x^2-4x+1$.

Short answer

The real solution of the quadratic equation is $x=2+\sqrt{3},2-\sqrt{3}$.

Step-by-step solution

Step 1. By method of quadratic formula.

The roots of the quadratic equation of the form $a{x}^2+bx+c=0$where $a\ne 0$can be evaluated by using the quadratic formula shown below.

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

Step 2. Find roots of quadratic equation by quadratic formula.

The given quadratic equation is $x^2-4x+1=0$whose roots can be evaluated by quadratic formula as shown below.

$$\begin{gathered} x=\frac{-\left(-4\right)\pm \sqrt{{\left(-4\right)}^2-4\left(1\right)\left(1\right)}}{2\left(1\right)} \\ =\frac{4\pm \sqrt{12}}{2} \\ =\frac{4\pm 2\sqrt{3}}{2} \\ =2+\sqrt{3},2-\sqrt{3} \end{gathered}$$

Step 3. DESCRIPTION OF STEPS.

The real solution of the equation is $x=2+\sqrt{3},2-\sqrt{3}$.