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KVPY2015MathematicsQuadratic Equation

If p(x) is a cubic polynomial with p(1)=3, p(0)=2 and p(-1)=4 , then _ -1 ¹ p(x) d x is

Options

  1. A2
  2. B3
  3. C4
  4. D5

Correct answer

D. 5

Step-by-step solution

p ( x )= ax ³+ b x ²+ cx + d p (0)=2 ~d =2 p (1)=3 a + b + c +2=3 a + b + c =1 p (-1)=4-a+b-c+2=4-a+b-c=22 b=3 b= 3 2 P(x)=a x³+ 3 2 x²+c x+2 _ -1 ¹ p(x) d x= _ -1 ¹ (a x²+ 3 2 x²+c x+2 ) d x=5

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