Completing the Square and Complex Solutions

Question

Write a quadratic equation with solutions that are not real numbers. Solve your equation.

Answer 1

x^2 = -1

x = + square root of -1 = +i

x= plus or minus i

Answer 2

If the discriminant b^2 - 4ac is less than zero then the solution will be imaginary numbers.

if a=b=c=1, then the discriminant will be -3

x^2 + x + 1

x = -1 +/- sqrt(1 - 4(1)(1))

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2

= -1 +/- sqrt(-3)

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2

= -1/2 +/- i*sqrt(3)/2