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AP EAMCET20226 Jul 2022Evening ShiftMathematicsQuadratic EquationActual

If one root of the quadratic equation a x^2+b x+c=0 is equal to the n th power of the other, then (a c^n )^ 1 / n+1 + (a^n c )^ 1 / n+1 =

Options

  1. A-2 b
  2. B-b
  3. Cb-1
  4. Db+1

Correct answer

B. -b

Step-by-step solution

Let and ^n are the roots of the equation aligned + & ^n=- b a and ^ n+1 = c a & = (a c^n )^ 1 n+1 + (a^n c )^ 1 n+1 & = [a (a ^ n+1 )^n ]^ 1 n+1 + (a^n a ^ n+1 )^ 1 n+1 & = [a^ n+1 ^ n(n+1) ]^ 1 n+1 + (a^ n+1 ^ n+1 )^ 1 n+1 & =a ^n+a =a ( ^n+ ) & a (- b a )=-b aligned

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