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

Question

express the answer in simplest radical form?

Answer 1

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