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KVPY2012MathematicsQuadratic Equation

Let a, b, c, d be numbers in the set 1,2,3,4,5,6 such that the curves y=2 x³+a x+b and y=2 x³+c x+d have no point in common. The maximum possible value of (a-c)²+b-d is -

Options

  1. A0
  2. B5
  3. C30
  4. D36

Correct answer

B. 5

Step-by-step solution

y=2 x³+a x+by=2 x³+c x+d No Solution array l 2 x³+a x+b 2 x³+c x+d a x+b c x+d for no real x (a-c) x d-b x d-b a-c a=c (a-c)²+(b-d)=0+6-1=5 array

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