Question

What are the roots of the polynomial function h(x)=3x2+243
?(1 point)
Responses

The roots are 9i and −9i.
The roots are 9i and −9i.

The roots are 9 and −9.
The roots are 9 and −9.

The roots are 81 and −81.
The roots are 81 and −81.

The roots are 81i and −81i.
The roots are 81i and −81i.

Answer 1

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

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

Subtracting 243 from both sides gives:

\[
3x^2 = -243
\]

Dividing both sides by 3 yields:

\[
x^2 = -81
\]

Taking the square root of both sides, we find:

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

The square root of \(-81\) can be expressed in terms of \(i\) (the imaginary unit):

\[
x = \pm 9i
\]

Thus, the roots of the polynomial function are \( 9i \) and \( -9i \).

The correct response is:

**The roots are 9i and −9i.**