Mathematics Solutions
(vi) \( 2x^2 – x – 4 = 0 \)
Sol.
\( 2x^2 – x – 4 = 0 \)
Comparing with \( ax^2 + bx + c = 0 \) we have \( a = 2, b = – 1, c = – 4 \)
$$ \begin{align} b^2 – 4ac &= (– 1)^2 – 4 (2) (– 4) \\ &= 1 + 32 \\ &= 33 \end{align} $$
By Formula method,
$$ x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a} $$
$$ x = \frac{-(-1) \pm \sqrt{33}}{2(2)} $$
$$ \therefore x = \frac{1 \pm \sqrt{33}}{4} $$
$$ \therefore x = \frac{1 + \sqrt{33}}{4} \quad \text{or} \quad \frac{1 - \sqrt{33}}{4} $$