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Use the discriminant to determine the number of solutions and types of solutions for the quadratic equation, below. Then answer the questions in the box. (4 points) x^2+ 8x = 13
A. Discriminant = _______________
B. Number of solutions for the quadratic equation = ________
C. Type of solutions (circle one): Real /Imaginary
D. Type of solutions (circle one): Rational/irrational

Respuesta :

kudzordzifrancis

Answer:

A. Discriminant = 116

B. Number of solutions for the quadratic equation = 2

C. Type of solutions (circle one):Imaginary

D. Type of solutions (circle one):irrational

Step-by-step explanation:

The given quadratic equation is

[tex] {x}^{2} + 8x = 13[/tex]

We rewrite in standard form to get;

[tex]{x}^{2} + 8x - 13 = 0[/tex]

The discriminant is

[tex]D = {b}^{2} - 4ac[/tex]

where a=1, b=8, c=-13

We substitute to get:

[tex]D = {8}^{2} - 4 \times 1 \times - 13[/tex]

[tex]D = 64 + 52[/tex]

[tex]D = 116[/tex]

Since the discriminant is great than zero, we have two distinct real roots

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