Question

what are all the solutions, both real and nonreal, to (4x^3 + 96x = 0)?

• (0, -2isqrt{6}, 2isqrt{6})
• (1, -2isqrt{6}, 2isqrt{6})
• (0, -4isqrt{6}, 4isqrt{6})
• (1, -4isqrt{6}, 4isqrt{6})

Explanation:

Factor out the greatest common factor

Using the Polynomial Equation Solving knowledge point

$$
LATEXBLOCK0
$$

Solve for the real root

Using the Polynomial Equation Solving knowledge point

$$
LATEXBLOCK1
$$

Solve for the nonreal roots

Using the Complex Roots of Polynomials knowledge point

$$
LATEXBLOCK2
$$

Combine all solutions

Using the Complex Roots of Polynomials knowledge point

$$ x = 0, \quad x = -2i\sqrt{6}, \quad x = 2i\sqrt{6} $$

Answer:

• (A) \(0, -2i\sqrt{6}, 2i\sqrt{6}\) (Correct answer)
• (B) \(1, -2i\sqrt{6}, 2i\sqrt{6}\)
• (C) \(0, -4i\sqrt{6}, 4i\sqrt{6}\)
• (D) \(1, -4i\sqrt{6}, 4i\sqrt{6}\)