no real solutions.
Work Step by Step
RECALL: A quadratic equation whose discriminant $b^2-4ac$ is negative has no real number solutions. The given quadratic equation has $a=1, b=2, $ and $c=5$. Solving for the discriminant gives: $b^2-4ac= 2^2-4(1)(5) = 4-20 = -16$ Since the discriminant is negative, the given equation has no real number solutions.