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AP EAMCET202017 Sep 2020Evening ShiftMathematicsQuadratic EquationActual

If the roots of the equation (a x^2+a x+c=0 ) are in the ratio (p: q ), then ( p q + q p = )

Options

  1. A( a^2 c )
  2. B( a 2 c )
  3. C( a c )
  4. D( a^2 2 c )

Correct answer

C. ( a c )

Step-by-step solution

Equation given be, ( aligned a x^2+a x+c & =0 Sum of roots =- a a & =-1 aligned ) ( ) Sum of roots (=- a a =-1 ) and product of roots (= c a ). Now roots are given in ratio ( p q ), i.e., ( = p q ) So, ( aligned p q + q p & = + & = + = -1 c a =- a c or a c aligned )

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