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