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KVPY2017MathematicsLinear Programming

Let f ( x ) be a polynomial with integer coefficients satisfying f (1)=5 and f (2)=7 . The smallest possible positive value of f (12) is

Options

  1. A5
  2. B7
  3. C27
  4. D15

Correct answer

C. 27

Step-by-step solution

f ( x )= ax + b 5= a + b 7=2 a + b solve a =2 ~b =3 f ( x )=2 x +3 f (12)=24+3 f (12)=27

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