Question

1. find the roots of the equation found below by using quadratic formula x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}

\\(x^2 - 4x + 1 = 0\\)
\\(x = \square\\)
show your work

Explanation:

Step1: Identify coefficients

For $x^2 - 4x + 1 = 0$, $a=1$, $b=-4$, $c=1$.

Step2: Calculate discriminant

$\Delta = b^2 - 4ac = (-4)^2 - 4(1)(1) = 16 - 4 = 12$.

Step3: Apply quadratic formula

$x = \frac{-b \pm \sqrt{\Delta}}{2a} = \frac{4 \pm \sqrt{12}}{2} = \frac{4 \pm 2\sqrt{3}}{2} = 2 \pm \sqrt{3}$.

Answer:

$2 + \sqrt{3}$ and $2 - \sqrt{3}$