Roots of a cubic with one root equal to the sum of the other two
Roots of a cubic with one root equal to the sum of the other two
6 marks
The roots of the cubic equation \(x^3-12x^2+44x+r=0\), where \(r\) is a constant, are \(\alpha\), \(\beta\) and \(\gamma\), with \(\alpha>\beta>\gamma\). It is also known that \(\alpha=\beta+\gamma\).
- Find \(\alpha\).[2]
- Show that \(\beta=4\) and find \(\gamma\).[3]
- Find \(r\).[1]
Solution:
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Answer:(a) \(\alpha=6\) (b) \(\gamma=2\) (c) \(r=-48\)
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