# Find the roots of the equation x ^ 3-121x = 0. If there are several roots, indicate the smallest root in your answer.

June 29, 2021 | education

| In this equation, x ^ 3 – 121 * x = 0, of course several roots, three roots, because the unknown x is in the third power. Let’s transform the initial equation. we get: x * (x ^ 2 – 121) = x * (x + √121) * (x – √121) = x * (x + 11) * (x – 11) = 0.

Equating each of the parentheses in turn to zero, we get: 1) x1 = 0; 2) (x + 11) = 0; x2 = -11; 3) (x – 11) = 0; x3 = 11.

Let’s arrange the roots as they grow: x: -11; 0; +11, and the smallest root would be x2 = -11.

Answer: x2 = -11.

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