Which systems of equations have no real number solutions? Check all that apply.

Set the two expressions for y equal in each system. A gives x² + 4x + 5 = 0, with discriminant 4² − 4(1)(5) = −4; C gives x² + 2x + 12 = 0, with discriminant 2² − 4(1)(12) = −44; and D gives x² − 2x + 3 = 0, with discriminant (−2)² − 4(1)(3) = −8. A quadratic with a negative discriminant has no real solutions, so these systems have no real intersections. B and E have positive discriminants, so each has real solutions.

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