Solve the following quadratic equation for x and give your answer correct to three significant figures :

Comparing equation 2x² - 10x + 5 = 0 with ax² + bx + c = 0, we get :

a = 2, b = -10 and c = 5

By formula,

⇒ x = $\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Substituting values we get :

$$\begin{aligned}\Rightarrow x = \frac{-(-10) \pm \sqrt{(-10)^2 - 4 \times 2 \times 5}}{2 \times 2} \\[1em] = \frac{10 \pm \sqrt{100 - 40}}{4} \\[1em] = \frac{10 \pm \sqrt{60}}{4} \\[1em] = \frac{10 \pm 2\sqrt{15}}{4} \\[1em] = \frac{2(5 \pm \sqrt{15})}{4} \\[1em] = \frac{5 \pm \sqrt{15}}{2} \\[1em] = \frac{5 \pm 3.87}{2} \\[1em] = \frac{5 + 3.87}{2}, \frac{5 - 3.87}{2} \\[1em] = \frac{8.87}{2}, \frac{1.13}{2} \\[1em] = 4.44, 0.565\end{aligned}$$

Hence, x = 4.44, 0.565