Question
Question
Solve the quadratic equation x2+16=0
. Express its solutions in the form a±bi
.(1 point)
Answers
GPT-4o mini
To solve the quadratic equation \( x^2 + 16 = 0 \), we start by isolating \( x^2 \):
\[
x^2 = -16
\]
Next, we take the square root of both sides. Since we are dealing with a negative number, we will introduce the imaginary unit \( i \), where \( i = \sqrt{-1} \):
\[
x = \pm \sqrt{-16}
\]
This can be rewritten as:
\[
x = \pm \sqrt{16} \cdot \sqrt{-1} = \pm 4i
\]
Thus, the solutions to the equation \( x^2 + 16 = 0 \) are:
\[
x = 0 \pm 4i
\]
This can be expressed in the form \( a \pm bi \) as:
\[
x = 0 \pm 4i
\]
So, the final solutions are:
\[
x = 0 + 4i \quad \text{and} \quad x = 0 - 4i
\]
\[
x^2 = -16
\]
Next, we take the square root of both sides. Since we are dealing with a negative number, we will introduce the imaginary unit \( i \), where \( i = \sqrt{-1} \):
\[
x = \pm \sqrt{-16}
\]
This can be rewritten as:
\[
x = \pm \sqrt{16} \cdot \sqrt{-1} = \pm 4i
\]
Thus, the solutions to the equation \( x^2 + 16 = 0 \) are:
\[
x = 0 \pm 4i
\]
This can be expressed in the form \( a \pm bi \) as:
\[
x = 0 \pm 4i
\]
So, the final solutions are:
\[
x = 0 + 4i \quad \text{and} \quad x = 0 - 4i
\]