The roots of a cubic - Math Central

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Question from Laura, a student:

Consider the equation x^3 + 6x^2 - x = 30.
One of the roots is equal to the sum of the other two roots.
Find the values of the three roots.

Hi Laura,

The product of the roots of x³ + 6x² - x - 30 is 30 so obvious candidates for the roots are ±2, ±3 and ±5. Substite these values into x³ + 6x² - x - 30 = 0 to see if any of them satisfy the equation. You will find 3 roots and one of them is the sum of the other two.

We don't see how to use the hint in the solution.

Chris and Harley

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