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Equal cubic roots (Posted on 2024-02-12)

It is known that two of the roots of the cubic equation x³ + 3x² − 9x + c = 0 are equal. If c > 0, find the value of c.

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Two equal roots occur at a place where the function has a slope of zero.

The derivative of the given function is 3*x^2 + 6*x - 9. Its zeros are x=-3 and 1.

At x=-3, c would need to be -27 to make the function zero at that point of zero slope.

At x = 1, c needs to be 5 to bring the function to zero when its derivative is zero.

As c needs to be positive, the answer is 5.

Posted by Charlie on 2024-02-12 12:57:56

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