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AP EAMCET2007MathematicsQuadratic Equation

If 1,2,3 and 4 are the roots of the equation x^4+a x^3+b x^2+c x+d=0 , then a+2 b+c is equal to

Options

  1. A-25
  2. B0
  3. C10
  4. D24

Correct answer

C. 10

Step-by-step solution

If 1,2,3,4 are the roots of the equation gathered x^4+a x^3+b x^2+c x+d=0, then (x-1)(x-2)(x-3)(x-4) =x^4+a x^3+b x^2+c x+d (x^2-3 x+2 ) (x^2-7 x+12 ) =x^4+a x^3+b x^2+c x+d x^4-10 x^3+35 x^2-50 x+24 =x^4+a x^3+b x^2+c x+d a=-10, b=35, c=-50, d=24 gathered Now, a+2 b+c=-10+2 35-50=10

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