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

A) Discriminant =  12

B) 2 Solutions

C) Real roots

D) Irrational solutions

Step-by-step explanation:

Given:

$x^2+ 8x = 13$

A) Discriminant:

The discriminant of the quadratic equation following $ax^2+bx+c=0$ is equal to $b^2 -4ac$. The notation used for the discriminant is Δ (delta), so we have $\Delta =b^2 -4ac.$

$x^2+ 8x = 13$

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

Now the Discriminant

$= (8)^2 - 4(1)(13)$

=  64 - 52

=  12

Thus $\Delta =$  12

B. Number of solutions for the quadratic equation

The Given equation is quadratic equation. The quadratic equation has a degree two. when the calculation of the discriminant is a positive number, the equation has two distinct roots.So the number of solutions is 2

C. Type of solutions (circle one):

A positive discriminant indicates that the quadratic has two distinct real number solutions.

Hence the roots are real

D. Type of solutions

The discriminant  is Real but they are not perfect squares . hence the Solutions are irrational