Question

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

Answer 1

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

${x}^{2} + 8x = 13$

We rewrite in standard form to get;

${x}^{2} + 8x - 13 = 0$

The discriminant is

$D = {b}^{2} - 4ac$

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

We substitute to get:

$D = {8}^{2} - 4 \times 1 \times - 13$

$D = 64 + 52$

$D = 116$

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