# How do you solve x^2 - 4x -3 = 0?

Aug 9, 2015

Use the quadratic formula to find $x = 2 \pm \sqrt{7}$

#### Explanation:

${x}^{2} - 4 x - 3$ is of the form $a {x}^{2} + b x + c$, with $a = 1$, $b = - 4$ and $c = - 3$.

This has discriminant $\Delta$ given by the formula:

$\Delta = {b}^{2} - 4 a c = {\left(- 4\right)}^{2} - \left(4 \times 1 \times - 3\right) = 16 + 12 = 28$

$= {2}^{2} \cdot 7$

This is positive but not a perfect square, so ${x}^{2} - 4 x - 3 = 0$ has two distinct irrational roots.

Use the quadratic formula to give the roots:

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

$= \frac{4 \pm 2 \sqrt{7}}{2} = 2 \pm \sqrt{7}$