Spencer Hodgson
04/27/2023 · Elementary School
4) FIND THE ROOTS OF \( y=x^{2}+4 \)
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Tutor-Verified Answer
Step-by-step Solution
To find the roots of the equation \( y = x^2 + 4 \), we need to set \( y \) to zero and solve for \( x \):
\[
0 = x^2 + 4
\]
Rearranging the equation gives:
\[
x^2 = -4
\]
To solve for \( x \), we take the square root of both sides:
\[
x = \pm \sqrt{-4}
\]
Since the square root of a negative number involves imaginary numbers, we can express this as:
\[
x = \pm 2i
\]
Thus, the roots of the equation \( y = x^2 + 4 \) are:
\[
x = 2i \quad \text{and} \quad x = -2i
\]
Quick Answer
The roots are \( x = 2i \) and \( x = -2i \).
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