Question

1. how many real solutions and how many non-real solutions does the equation \\(x^2+5=0\\) have? describe what implications your answer has for graphing the function \\(y=x^2+5\\).

1. solve the quadratic equation using your choice of the methods we learned in this module. indicate which method you are using, and show your work.

\\4x^2 - 22 = x^2 + 5\\

Explanation:

Solve the first equation and determine root types

$$
LATEXBLOCK0
$$

The equation has \(0\) real solutions and \(2\) non-real (complex) solutions.
Since there are no real solutions, the graph of \(y = x^2 + 5\) has no \(x\)-intercepts and does not cross or touch the \(x\)-axis.

Solve the second quadratic equation

$$
LATEXBLOCK1
$$

The method used is solving by taking square roots.

Answer:

Question 2

The equation \(x^2+5=0\) has \(0\) real solutions and \(2\) non-real solutions. This implies that the graph of the function \(y=x^2+5\) has no \(x\)-intercepts and does not intersect the \(x\)-axis.

Question 3

Method: Solving by taking square roots.

$$
LATEXBLOCK0
$$

The solutions are \(x = 3\) and \(x = -3\).