If x1 and x2 are the arithmetic and harmonic means of the roots of the equation ax2+bx+c=0, the equation whose quadratic roots are x1 and  x2, is

If x1 and x2 are the arithmetic and harmonic means of the roots of the equation ax2+bx+c=0, the equation whose quadratic roots are x1 and  x2, is

  1. A

    abx2+(b2+ac)x+bc=0

  2. B

    2abx2+(b2+4ac)x+2bc=0

  3. C

    2abx2+(b2+ac)x+bc=0

  4. D

    None of the above 

    Register to Get Free Mock Test and Study Material

    +91

    Verify OTP Code (required)

    I agree to the terms and conditions and privacy policy.

    Solution:

    Let α and β be the roots of  ax2+bx+c=0

     x1=α+β2=b2a x2=2αβα+β=2caba=2cb

    The required equation is

    x2[(b2a)+(2cb)]x+2bc2ab=02abx2+(b2+4ac)x+2bc=0

    Chat on WhatsApp Call Infinity Learn

      Register to Get Free Mock Test and Study Material

      +91

      Verify OTP Code (required)

      I agree to the terms and conditions and privacy policy.