Use the discriminant to determine the number and type of solutions to the quadratic equation and solve the questions below. Show all work for full credit.

a^2+8a=13

A: Discriminant:
B: Number of Solutions:
C: Type of solutions (real or imaginary):
D: Type of solutions (rational or irrational):

For this case we have the following quadratic equation:

Where:

The discriminant is given by:

then we have two different real roots.

We have to, based on the quadratic formula:

Thus, the solution will be irrational.

Two real solutions

Irrational solutions

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step-by-step explanation:

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,