Question

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

Answer 1

(x -1)² – 3x + 4 = 0
x² + 1 - 2x - 3x + 4 = 0
x² - 5x + 5 = 0
Comparing it with
ax² + bx + c = 0, we get
a = 1, b = -5, c = 5
By using the formula,
x = `(-b ± sqrt(b^2 - 4ac))/(2ac)`

= `(5 ± sqrt(25 - 20))/(2)`

= `(5 ± sqrt(5))/(2)`

x = `(5 ± 2·24)/(2)`
Taking +ve sign x = `(5 + 2·24)/(2)`
x = 3·62
Taking -ve sign x = `(5 - 2·25)/(2)`
= `(2·76)/(2)`
 =1·38
Thus required value are 3·62 and 1·38.