1. **State the problem:** Find the zeroes of the function $$f(x) = (x^2 + 2)(x^2 + 1)$$. 2. **Formula and rules:** The zeroes of a product of factors occur when any factor equals zero. So, solve each factor separately: $$x^2 + 2 = 0$$ $$x^2 + 1 = 0$$ 3. **Solve the first factor:** $$x^2 + 2 = 0 \implies x^2 = -2 \implies x = \pm \sqrt{-2} = \pm i\sqrt{2}$$ 4. **Solve the second factor:** $$x^2 + 1 = 0 \implies x^2 = -1 \implies x = \pm \sqrt{-1} = \pm i$$ 5. **Interpretation:** The zeroes are complex numbers because the expressions under the square roots are negative. 6. **Final answer:** The zeroes of $$f(x)$$ are $$x = \pm i\sqrt{2}$$ and $$x = \pm i$$.