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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.

No Solution Yet Submitted by Danish Ahmed Khan

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some thoughts

Comment 3 of 3 |

A rough and ready approach:

Trying small solutions,

x^3+3x^2-9x+c = (x-1)(x-1)(x-z) looks promising.

x^3+3x^2-9x+c = x^3-x^2z-2x^2+2xz+x-z

Simplifying x^2(z+5)+z = 2x(z+5)-c, a nice expression.

Let z=-5, then this simplifies to z=-c, giving c=5

Posted by broll on 2024-02-12 21:32:40

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