Solve for x using the quadratic formula. Write your answer correct to two significant figures : (x - 1)² - 3x + 4 = 0 .

Given,

$(x - 1)^2 - 3x + 4 = 0 \\[0.5em] \Rightarrow x^2 + 1 - 2x - 3x + 4 = 0 \\[0.5em] \Rightarrow x^2 - 5x + 5 = 0$

Comparing it with ax² + bx + c = 0
a= 1, b = -5, c = 5

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

$\Rightarrow \dfrac{-(-5) ± \sqrt{(-5)^2 - 4 \times 1 \times 5}}{2 \times 1} \\[1em] \Rightarrow \dfrac{5 ± \sqrt{25 - 20}}{2} \\[1em] \Rightarrow \dfrac{5 + \sqrt{5}}{2} \text{ or } \dfrac{5 - \sqrt{5}}{2} \\[1em] \Rightarrow \dfrac{5 + 2.2}{2} \text{ or } \dfrac{5 - 2.2}{2} \\[1em] \Rightarrow \dfrac{7.2}{2} \text{ or } \dfrac{2.8}{2} \\[1em] 3.6 \text{ or } 1.4$

Hence, roots of the given equation are 3.6, 1.4.