Question

2x² – x – 4 = 0

Answer 1

Given: 2x² – x – 4 = 0
On comparing this equation with ax² + bx + c = 0, we get:
a = 2, b = –1 and c = –4
For the quadratic equation ax² + bx + c = 0, we know that the quadratic formula is

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
On substituting a = 2, b = –1 and c = –4, we get:
$$\begin{gathered} x=\frac{-\left(-1\right)\pm \sqrt{{\left(-1\right)}^2-4\times 2\times \left(-4\right)}}{2\times 2} \\ =\frac{1\pm \sqrt{33}}{4} \end{gathered}$$
Thus, the solution of the given quadratic equation is x = $\frac{1+\sqrt{33}}{4},\frac{1-\sqrt{33}}{4}$.