Find all zeros of the function f(x) = x²(x + 1)(x³ - 64). A)x = 0, 1, -4 B)x = 0, -1, 4 C)x = -1, 64 D)x = 1, -64 E)x = 0, -1, 4, $- 2 - 2 \sqrt { 3 } i$ , $- 2 + 2 \sqrt { 3 } i$

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Quizplus · Accepted Answer

The function can be rewritten as $f(x) = x^2(x + 1)(x^3 - 64)$. Setting $f(x) = 0$ gives the zeros at $x = 0$ (from $x^2$), $x = -1$ (from $x + 1$), and $x^3 - 64 = 0$ which gives $x = 4$ (since $4^3 = 64$). The cubic equation $x^3 - 64 = 0$ also has complex roots, which are found by factoring or using the cubic formula, resulting in $-2 - 2\sqrt{3}i$ and $-2 + 2\sqrt{3}i$.

Find All Zeros of the Function F(x) = X2(x −2−23i- 2 - 2 \sqrt { 3 } i−2−23​i

Find All Zeros of the Function F(x) = X²(x $- 2 - 2 \sqrt { 3 } i$