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Manipal MET2018MathematicsQuadratic Equation

The condition that one root of the equation a x^2+b x+c=0 may be square of the other, is

Options

  1. Aa^2 c+a c^2+b^3-3 a b c=0
  2. Ba^2 c^2+a c^2+b^2-3 a b c=0
  3. Ca c^2+a c-b^3-3 a b c=0
  4. Da^2 c+a c^2-b^3-3 a b c=0

Correct answer

A. a^2 c+a c^2+b^3-3 a b c=0

Step-by-step solution

Let one root of equation a x^2+b x+c=0 is then another root will be ^2 . + ^2=- b a and array ll and & ^2 = c a & ^3 array = c a From Eq. (i), array cc & ( + ^2 )^3=- b^3 a^3 & ^3+ ^6+3 ^3 ( + ^2 )=- b^3 a^3 & c a + c^2 a^2 +3 c a (- b a )=- b^3 a^3 & a^2 c+a c^2-3 a b c+b^3=0 array

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