Solve the following quadratic equation 2x2 − 5x − 4 = 0. Give your answer correct to three significant figures.
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Given,
⇒ 2x2 − 5x − 4 = 0
Comparing equation 2x2 − 5x − 4 = 0 with ax2 + bx + c = 0, we get :
a = 2, b = -5 and c = -4.
By formula,
x = $\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Substituting values we get :
$$\begin{aligned}\Rightarrow x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4 \times (2) \times (-4)}}{2 \times (2)} \\[1em] = \frac{5 \pm \sqrt{25 - (-32)}}{4} \\[1em] = \frac{5 \pm \sqrt{25 + 32}}{4} \\[1em] = \frac{5 \pm \sqrt{57}}{4} \\[1em] = \frac{5 + \sqrt{57}}{4} \text{ or } \frac{5 - \sqrt{57}}{4} \\[1em] = \frac{5 + 7.55}{4} \text{ or } \frac{5 - 7.55}{4} \\[1em] = \frac{12.55}{4} \text{ or } \frac{-2.55}{4} \\[1em] = 3.14 \text{ or } -0.638\end{aligned}$$
Hence, x = 3.14, -0.638.