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KVPY2011MathematicsQuadratic Equation

Let f(x)=x¹²-x⁹+x⁴-x+1 . Which of the following is true?

Options

  1. Af is one-one
  2. Bf has a real root
  3. Cf ^ never vanishes.
  4. Df takes only positive values

Correct answer

D. f takes only positive values

Step-by-step solution

aligned f(x) &=x⁹ (x³-1 )+x (x³-1 )+1 positive for x 1 or x 0 &=1-x+x⁴-x⁹+x¹² positive for x (0,1) aligned f ( x ) is always positive

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