Question

Solve the following quadratic equation.

x² - 4x - 3 = 0

Answer 1

x² - 4x - 3 = 0

Δ = b² - 4ac

= (-4)² - 4(1)(-3)

= 16 + 12

= 28

\[\Rightarrow x = \frac{- \left( - 4 \right) \pm \sqrt{\left( - 4 \right)^2 - 4 \times 1 \times \left( - 3 \right)}}{2 \times 1}\]

\[ \Rightarrow x = \frac{4 \pm \sqrt{16 + 12}}{2}\]

\[ \Rightarrow x = \frac{4 \pm \sqrt{28}}{2}\]

\[ \Rightarrow x = \frac{4 \pm 2\sqrt{7}}{2}\]

\[ \Rightarrow x = 2 \pm \sqrt{7}\]

The roots of the given quadratic equation are

`2+sqrt7 and 2-sqrt7`