Solve the quadratic equation (x − 2)2 − 5x − 3 = 0 and give your answer correct to 3 significant figures.
Show SolutionHide Solution↓
Given,
⇒ (x − 2)2 − 5x − 3 = 0
⇒ x2 - 4x + 4 − 5x − 3 = 0
⇒ x2 - 9x + 1 = 0
Comparing x2 - 9x + 1 = 0 with ax2 + bx + c = 0 , we get :
a = 1, b = -9 and c = 1
By formula,
$$\begin{aligned}\Rightarrow x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \\[1em] \Rightarrow x = \frac{-(-9) \pm \sqrt{(-9)^2 - 4(1)(1)}}{2(1)} \\[1em] \Rightarrow x = \frac{9 \pm \sqrt{81 - 4}}{2} \\[1em] \Rightarrow x = \frac{9 \pm \sqrt{77}}{2} \\[1em] \Rightarrow x = \frac{9 \pm 8.775}{2} \\[1em] \Rightarrow x = \frac{9 + 8.775}{2} \text{ or } \frac{9 - 8.775}{2} \\[1em] \Rightarrow x = \frac{17.775}{2} \text{ or } \frac{0.225}{2} \\[1em] \Rightarrow x = 8.8875 \text{ or } 0.1125 \\[1em] \Rightarrow x = 8.89 \text{ or } 0.113\end{aligned}$$
Hence, x = 8.89 or 0.113.