Solve the equation 5x² - 3x - 4 = 0 and give your answer correct to 3 significant figures.

The given equation is 5x² - 3x - 4 = 0.

Comparing it with ax² + bx + c = 0, we get
a = 5 , b = -3 , c = -4

By using formula, $x = \dfrac{-b ± \sqrt{b^2 - 4ac}}{2a}$

we obtain:

$\Rightarrow x = \dfrac{-(-3) ± \sqrt{(-3)^2 - 4\times 5 \times -4}}{2 \times 5} \\[1em] \Rightarrow x = \dfrac{3 ± \sqrt{9 + 80}}{10} \\[1em] \Rightarrow x = \dfrac{3 ± \sqrt{89}}{10} \\[1em] \Rightarrow x = \dfrac{3 + \sqrt{89}}{10} \text{ or } \dfrac{3 - \sqrt{89}}{10} \\[1em] \text{ Also } \sqrt{89} = 9.434 (\text{From tables}) \\[1em] \Rightarrow x = \dfrac{3 + 9.434}{10} \text { or } \dfrac{3 - 9.434}{10} \\[1em] \Rightarrow x = \dfrac{12.434}{10} \text{ or } \dfrac{-6.434}{10} \\[1em] \Rightarrow x = 1.2434 \text{ or } -0.6434 \\[1em] \Rightarrow x = 1.24 \text{ or } -0.643 \text{ (correct to three significant figures) }$

Hence roots of the given equations are 1.24 , -0.643.