GATE ME 2022 Set 2 — Question 15
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Engineering Mathematics → Single Variable Calculus → Functions of Single Variable
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Question
A polynomial of degree with constant real coefficients has triple roots at . Which one of the following conditions must be satisfied?
Correct answer
(B) φ(s) = 0, (dφ(s))/(ds) = 0, and (d²φ(s))/(ds²) = 0 at s = -σ
Solution
If a polynomial has a root of multiplicity at , then the function and its first derivatives must vanish at that point. That is, .
For a triple root () at , the conditions are:
For a triple root () at , the conditions are:
1.
2.
3.
This matches option (B).Continue learning with Success Tracker
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