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

`(x - 1)^2 - 3x + 4 = 0`

`=> x^2 - 2x + 1 - 3x + 4 = 0`

`=> x^2 - 5x + 5 = 0`

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

`x = (-b+- sqrt(b^2 - 4ac))/"2a"`

In the given equation,

a = 1, b = –5, c = 5

Thus, the roots of the equation are

`x= (-(-5)+- sqrt((-5)^2 -4(1(5))))/(2(1))`

`=> X = (5 +- sqrt(25 - 20))/2`

`=>  x = (5+ sqrt5)/2`

`=> x = (5 + sqrt5)/2  or x = (5-sqrt5)/2`

⇒ x = 3.618 or x = 1.382

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