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KVPY2014MathematicsQuadratic Equation

The under of integers n for which 3 x³-25 x+n=0 has three real roots is

Options

  1. A1
  2. B25
  3. C55
  4. DInfinite

Correct answer

C. 55

Step-by-step solution

Let f(x)=3 x³-25 xf^ (x)=9 x²-25f^ (x)=0 5 3 f(-5 / 3)=250 / 9 27.7f(5 / 3)=-250 / 9 -27.7 n can take 55 values

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