Official papers

Official 2021 Paper 2 · Q6

Paper 2Algebra

Consider the following two statements about the polynomial f(x)f(x):

  • PP: f(x)=0f(x)=0 for exactly three real values of xx
  • QQ: f′(x)=0f'(x)=0 for exactly two real values of xx

Which one of the following is correct?

APP is necessary but not sufficient for QQ.
BPP is sufficient but not necessary for QQ.
CPP is necessary and sufficient for QQ.
DPP is not necessary and not sufficient for QQ.

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