Question

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

Answer 1

The given quadratic equation is

${\displaystyle {(x-1)}^2-3x+4=0}$

${\displaystyle \Rightarrow x^2-2x+1-3x+4=0}$

${\displaystyle \Rightarrow x^2-5x+5=0}$

The roots of the quadratic equation ax² + bx + c = 0 are given by

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

In the given equation,

a = 1, b = –5, c = 5

Thus, the roots of the equation are

${\displaystyle x=\frac{-(-5)\pm \sqrt{{(-5)}^2-4\left(1\left(5\right)\right)}}{2\left(1\right)}}$

${\displaystyle \Rightarrow X=\frac{5\pm \sqrt{25-20}}{2}}$

${\displaystyle \Rightarrow x=\frac{5+\sqrt{5}}{2}}$

${\displaystyle \Rightarrow x=\frac{5+\sqrt{5}}{2} \text{or}x=\frac{5-\sqrt{5}}{2}}$

⇒ x = 3.618 or x = 1.382

⇒ x = 3.6 or x = 1.4 (correct to two significant figures)