Solve Using the Quadratic Formula x^2-x+1=0

Problem

x2−x+1=0

Solution

1. Identify the coefficients a b and c from the quadratic equation in the form a*x2+b*x+c=0

a=1

b=−1

c=1

2. State the quadratic formula used to find the roots of the equation.

x=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the values of a b and c into the formula.

x=(−(−1)±√(,(−1)2−4*(1)*(1)))/(2*(1))

4. Simplify the expression inside the square root (the discriminant).

x=(1±√(,1−4))/2

x=(1±√(,−3))/2

5. Apply the imaginary unit i=√(,−1) to handle the square root of the negative number.

x=(1±i√(,3))/2

Final Answer

x=(1±i√(,3))/2

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