Doubt

Question

A polynomial of degree 4 with real coefficients

A) Can possibly have no extrema and no zero crossings

B) May have up to four extrema and up to 3 zero crossings

C) Cannot have more than three extrema and more than four zero crossings

D) Will have an equal number of extrema and zero crossings

Comments

c????

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yeah but how ?

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Degree 4 polynomial will have 4 roots means 4 zero crossing and max of 3 max values think of cos function but here its given as real coeff that doesnot make any difference

This pic is just for visualization not actual but eventually this is the best case where red dots are extremas and toching x axis are zero points.

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A polynomial of degree 4 so at most 4 real roots(means zero crossing) and at most three extrema

Answer 1

https://gateoverflow.in/?qa=blob&qa_blobid=6809098301494191150