If a and b are the roots of the equation x^2 - x + 1 = 0

• Quadratic Equations

If a and b are the roots of the equation x² - x + 1 = 0, then a²⁰⁰⁹ + b²⁰⁰⁹ is equal to

1. -2
2. 2
3. -1
4. 1

Answer

x² - x + 1 = 0

x = 1/2 + √3/2i , 1/2 - √3/2i

a = e^iπ/3 , b = e^-iπ/3

Putting values of a and b:

= 2cos(669 + 2/3)π

The correct option is D.