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 $-9i$.