TMUA 2023 Paper 2 Q19 — Worked Solution

P2·Differentiation, Functions, Transformations & Graphs·6.5Official · 2023 · Q19

roots-and-stationary-pointspolynomialmust-be-true

In this question,

f (x)

is a non-constant polynomial, and

g (x) = x f^{'} (x)

f (x) = 0

for exactly

M

real values of

x

g (x) = 0

for exactly

N

real values of

x

.Which of the following statements is/are true?

It is possible that

M < N

It is possible that

M = N

III

It is possible that

M > N

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