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Question
Solve for x using the quadratic formula. Write your answer correct to two significant figures:
(x – 1)2 – 3x + 4 = 0
Solution
(x – 1)2 – 3x + 4 = 0
x2 – 2x + 1 – 3x + 4 = 0
x2 – 5x + 5 = 0
Here a = 1, b = – 5 and c = 5
∴ `x = (-b +- sqrt(b^2 - 4ac))/(2a)`
` x = (-(5) ± sqrt((-5)^2 - 4(1)(5)))/(2)`
= `(5 ± sqrt(25 - 20))/(2)`
= `(5 ± sqrt(5))/(2)`
= `(5 + 2.236)/(2)` or `(5 - 2.236)/(2)`
= `(7.236)/(2)` or `(2.764)/(2)`
= 3.618 or 1.382
∴ x = 3.618 ≈ 3.6 or 1.382 ≈ 1.4
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