Which of the following polynomials has solutions that are not real numbers?

Assuming this question associates "solutions" with "zeros", then the answer is

   x^2 + 2x + 3 



If we set x^2 + 2x + 3 to equal 0, we have

   x^2 + 2x + 3 = 0

The discriminant of this equation of the form ax² + bx + c = 0 is

   discriminant = b² - 4ac = 2^2 - 4(1)(3) = -8

The discriminant is negative, so there are no real solutions (the discriminant is under a square root in the quadratic equation; square root of a negative number is not a real number)