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Let f:[0,1] R be a continuous function and P be a polynomial of degree 4 with coefficients in R . If P(f(x))=0 for all x R , then

Options

  1. Af(x)=0 for all x R .
  2. Bf is a constant function.
  3. Cfor all continuous functions g , there exists x [0,1] such that P(g(x))=0 .
  4. DP has at most two roots which do not belong to R .

Correct answer

D. P has at most two roots which do not belong to R .

Step-by-step solution

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