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AP EAMCET201726 Apr 2017Morning ShiftMathematicsQuadratic EquationActual

If the roots of the equation x^3-7 x^2+14 x-8=0 are in geometric progression, then the difference between the largest and the smallest roots is

Options

  1. A4
  2. B2
  3. C1 2
  4. D3

Correct answer

D. 3

Step-by-step solution

Given equation, x^3-7 x^2+14 x-8=0 Let the roots of this equation are a r , a, a r . Then, we get Sum of roots =7 From Eq. (iii), we get a=2 Now, from Eq. ( i) , we get aligned & 2 r +2 r=5 & 2+2 r^2=5 r & 2 r^2-5 r+2=0 & 2 r^2-4 r-r+2=0 & 2 r(r-2)-1(r-2)=0 & (r-2)(2 r-1)=0 & r=2 or r= 1 2 aligned Thus, the roots are 1, 2, 4 . Hence, difference of largest and smallest number =4-1=3

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