What are the roots of f(x) = x2 – 48?

–48 and 48
–24 and 24
Negative 8 StartRoot 3 EndRoot and 8 StartRoot 3 EndRoot
Negative 4 StartRoot 3 EndRoot and 4 StartRoot 3 EndRoot

1 answer

To find the roots of the function \( f(x) = x^2 - 48 \), we set \( f(x) \) equal to zero:

\[ x^2 - 48 = 0 \]

Next, we solve for \( x^2 \):

\[ x^2 = 48 \]

Taking the square root of both sides gives:

\[ x = \pm \sqrt{48} \]

We can simplify \( \sqrt{48} \):

\[ \sqrt{48} = \sqrt{16 \cdot 3} = \sqrt{16} \cdot \sqrt{3} = 4\sqrt{3} \]

Thus, the roots are:

\[ x = 4\sqrt{3} \quad \text{and} \quad x = -4\sqrt{3} \]

Therefore, the roots of the function \( f(x) = x^2 - 48 \) are \( -4\sqrt{3} \) and \( 4\sqrt{3} \).

Among the given options, the correct answer is:

Negative 4 StartRoot 3 EndRoot and 4 StartRoot 3 EndRoot.