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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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Puzzle Solution

| Comment 2 of 3 |

a+2b=-3, b^2+2ab= -9, c= -a*b^2

=> b^2+2(-3-2b)b = -9

=> -3b^2= -3

=> b= +/-1

=> a = -3 -2b = -1, -5

Thus, c = (-1), -(-5)

=-1, 5

Since c>0, it follows that: c=5

Posted by K Sengupta on 2024-02-12 21:28:33

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