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AP EAMCET201726 Apr 2017Morning ShiftMathematicsQuadratic EquationActual

The harmonic mean of two numbers is - 8 5 and their geometric mean is 2 . The quadratic equation whose roots are twice those numbers is

Options

  1. Ax^2+5 x+4=0
  2. Bx^2+10 x+16=0
  3. Cx^2-10 x+16=0
  4. Dx^2-5 x+4=0

Correct answer

B. x^2+10 x+16=0

Step-by-step solution

Let two numbers be a and b G.M. = a b =2 Now, H.M. = 2 a b a+b =- 8 5 2 4 a+b =- 8 5 (from Eq. (i)) a+b=-5 Here, roots are twice of these numbers. So, aligned & (2 a)(2 b)=4 a b=4 4=16 & 2 a+2 b=2(a+b)=2 -5=-10 aligned Quadratic Equation x^2+10 x+16=0

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