Clavis TMUA Set B Paper 2 · Question 18

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Clavis TMUA Set B Paper 2 · Q18

Paper 2Logic & proofFunctions & graphsAlgebra

The function $f$ is a non-zero polynomial defined for all real $x$ .

Which one of the following is a necessary condition for the equation $f(x)=0$ to have at least two distinct real roots?

f

has degree at least

3

f(0)=0

f''(x)=0

has at least one real solution

f'(x)<0

for all real

x

f'(x)=0

has at least one real solution

f

has even degree

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