The roots of equation $x^{3}+4x^{2}-4x-16=0$ are
- $-4, -2, 2$
- $-6, -3, 2$
- $2, 2, 4$
- $-1, -2, 2$
Reveal answer
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A
Correct answer
Explanation
Factoring the equation x^3 + 4x^2 - 4x - 16 = 0: x^2(x + 4) - 4(x + 4) = 0, which becomes (x^2 - 4)(x + 4) = 0. This factors further to (x - 2)(x + 2)(x + 4) = 0. The roots are 2, -2, and -4.
AI explanation
We look for rational roots using the factors of the constant term, 16. Testing x = 2 gives (8) + 4(4) - 4(2) - 16 = 8 + 16 - 8 - 16 = 0, confirming x = 2 is a root. We divide the cubic polynomial by (x - 2) to get the quadratic x^2 + 6x + 8. Factoring this quadratic yields (x + 4)(x + 2) = 0, giving the remaining roots as -4 and -2.