To find the roots of the equation f(x) = x² – 48, we need to set the function equal to zero:
x² – 48 = 0
Next, we can rearrange this equation to isolate x²:
x² = 48
Now, we can find the roots by taking the square root of both sides. Remember that taking the square root has both a positive and a negative solution:
x = ±√48
We can further simplify √48. Since 48 can be factored into 16 × 3, we recognize that 16 is a perfect square:
√48 = √(16 × 3) = √16 × √3 = 4√3
Thus, the roots can be expressed as:
x = 4√3 and x = -4√3
In summary, the roots of the equation f(x) = x² – 48 are:
- x = 4√3
- x = -4√3