Question

what are the roots of f(x) = x² - 48?
○ -48 and 48
○ -24 and 24
○ -8√3 and 8√3
○ -4√3 and 4√3

Explanation:

Step1: Set the function to zero

To find the roots of \( f(x) = x^2 - 48 \), we set \( f(x) = 0 \), so we have the equation \( x^2 - 48 = 0 \).

Step2: Solve for \( x \)

Add 48 to both sides of the equation: \( x^2 = 48 \).
Then take the square root of both sides. Remember that if \( x^2 = a \) (where \( a \geq 0 \)), then \( x = \pm\sqrt{a} \). So \( x = \pm\sqrt{48} \).
Simplify \( \sqrt{48} \): we can factor 48 as \( 16\times3 \), so \( \sqrt{48}=\sqrt{16\times3}=\sqrt{16}\times\sqrt{3}=4\sqrt{3} \).
Therefore, the roots are \( x = - 4\sqrt{3} \) and \( x = 4\sqrt{3} \).

Answer:

-4√3 and 4√3 (the option with this pair)