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If the equations x^(3) - mx^2 - 4 = 0 a...

If the equations `x^(3) - mx^2 - 4 = 0 and x^(3) + mx + 2 = 0 .m in R` have one common root, then find the values of m.

Text Solution

Verified by Experts

The correct Answer is:
-3
We have
`x^(3) - mx^(2) - 4 = 0` (1) and `x^(3) + mx + 2 = 0` (2)
Multiplying (2) by x and adding with (1), we get
` x^(4) + x^(3) + 2x - 4 = 0`
`rArr (x -1) (x + 2) (x^(2) + 2) = 0`
So, common root can be x = 1 or x = -2
If x = 1 , then m = -3
If x = - 2 , then m = -3.
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