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AP EAMCET2012MathematicsQuadratic Equation

Let A= | array cc 2 & e^ i -1 & i²⁰¹² array |, C= d d x ( 1 x )_ x=1 , D= _ e^2 ^1 d x x If the sum of two roots of the equation A x^3+B x^2+C x-D=0 is equal to zero, then B is equal to

Options

  1. A-1
  2. B0
  3. C1
  4. D2

Correct answer

D. 2

Step-by-step solution

Given, aligned A & = | array cc 2 & e^ i -1 & i²⁰¹² array | & = | array cc 2 & +i -1 & (1^4 )⁵⁰³ array | aligned aligned & = | array cc 2 & -1 -1 & 1 array |=2-1=1 C & = d d x ( 1 x )_ x=1 = (- 1 x^2 )_ x=1 =-1 aligned and aligned D & = _ e^2 ^1 d x x & =[ x]_ e^2 ^1 & = 1- e^2=0-2 & =-2 aligned Let , and are the roots of the equation aligned & A x^3+B x^2+C x+D=0 & x^3+B x^2-x+2=0 & + + =-B & =-B ( + =0 given ) aligned -B satisfies the Eq. (ii), array ll & (-B)^3+B^2+B+2=0 & B=2 array

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