Question

What are the roots of the polynomial function h(x)=3x^2+243 ? (1 point) The roots are 9 and -9. The roots are 81 and -81. The roots are 9i and -9i. The roots are 81i and -81i.

Answer 1

To find the roots of the polynomial function \( h(x) = 3x^2 + 243 \), we need to set the equation equal to zero:

\[
3x^2 + 243 = 0
\]

First, we can isolate \( x^2 \):

\[
3x^2 = -243
\]

Now, divide both sides by 3:

\[
x^2 = -81
\]

To find \( x \), take the square root of both sides:

\[
x = \pm \sqrt{-81} = \pm \sqrt{81} \cdot \sqrt{-1}
\]

Since \( \sqrt{81} = 9 \) and \( \sqrt{-1} = i \), we get:

\[
x = \pm 9i
\]

Thus, the roots of the polynomial function \( h(x) = 3x^2 + 243 \) are:

**The roots are \( 9i \) and \( -9i \).**