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AP EAMCET202420 May 2024Morning ShiftMathematicsQuadratic EquationActual

If P (x)=x^5+a x^4+b x^3+c x^2+d x+e is a polynomial such that P (0)=1, P (1)=2, P (2)=5, P (3)=10 and P (4)=17 , then P (5)=

Options

  1. A26
  2. B146
  3. C126
  4. D76

Correct answer

B. 146

Step-by-step solution

P(x)=x^5+a x^4+6 x^3+c x^2+d x+eP(x)-x^2-1 is a polynomial of degree 5 and has 5 roots 0,1,2,3,4P(x)-x^2-1=(x-0)(x-1)(x-2)(x-3)(x-4)P(x)=x(x-1)(x-2)(x-3)(x-4)+x^2+1P(5)=5!+25+1=146

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