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Equal cubic roots (
Posted on 20240212
)
It is known that two of the roots of the cubic equation x
^{3}
+ 3x
^{2}
− 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^29x+c = (x1)(x1)(xz) looks promising.
x^3+3x^29x+c = x^3x^2z2x^2+2xz+xz
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 20240212 21:32:40
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