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Solve the equation x^2-x+1=0

0 votes

express the answer in simplest radical form?

asked Feb 7, 2013 in ALGEBRA 1 by angel12 Scholar

1 Answer

+1 vote

x2 - x + 1 = 0

Compare equation with standard from ax2 + bx + c = 0 and write the coefficients.

a = 1, b = -1 and c = 1.

Now using quadratic formula: x = [-b ± √(b2 - 4ac)] / 2a

Substitute a = 1, b = -1 and c = 1 in the quadratic formula.

x = [-(-1) ± √(-1)2 - 4(1)(1)] / 2(1)

x = [1 ± √(1 - 4)] / 2

x = [1 ± √(-3)] / 2

An imaginary number is i2 = -1

x = [1 ± √(i23)] / 2

x = [1 ± i√(3)] / 2

x = [1 + i√(3)] / 2 or x = [1 - i√(3)] / 2

Therefore x = [1 + i√(3)] / 2 or x = [1 - i√(3)] / 2

answered Feb 7, 2013 by richardson Scholar

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