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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):

Respuesta :

carlosego

For this case we have the following quadratic equation:

[tex]a ^ 2 + 8a-13 = 0[/tex]

Where:

[tex]a = 1\\\b = 8\\c = -13[/tex]

The discriminant is given by:

[tex]d = b ^ 2-4ac\\d = 8 ^ 2-4 (1) (- 13)\\d = 64 + 52\\d = 116[/tex]

[tex]d> 0,[/tex] then we have two different real roots.

We have to, based on the quadratic formula: [tex]\sqrt {116} = \sqrt {4 * 29} = 2 \sqrt {29}[/tex]

Thus, the solution will be irrational.

Answer:

[tex]d = 116[/tex]

Two real solutions

Irrational solutions