If the discriminating of a quadratic equation is equal to -8, which statement describes the roots?
a. there are two complex roots
b. there are two real roots
c. there is one real root
d. there is one complex root

A. There are two complex roots

A. there are two complex roots

the discriminant is smaller than 0, so does not have real roots. Except when discriminant=0, every other numbers have two solution whether it is complex or real.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.