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AP EAMCET2007MathematicsQuadratic Equation

If and are the roots of the equation a x^2+b x+c=0 and, if p x^2+q x+r=0 has roots 1- and 1- , then r is equal to

Options

  1. Aa+2 b
  2. Ba+b+c
  3. Ca b+b c+c a
  4. Da b c

Correct answer

B. a+b+c

Step-by-step solution

Since, , are the roots of the equation a x^2+b x+c=0 . + =- b a = c a The quadratic equation whose roots are 1- and 1- , is aligned & x^2- ( 1- + 1- ) x+ 1- 1- =0 & x^2- ( - + - ) x & x^2- ( - b a -2 c a c a ) x+ 1- (- b a )+ c a c a =0 aligned x^2- ( - b a -2 c a c a ) x+ 1- (- b a )+ c a c a =0 from Eq. (i) aligned & x^2- (-b-2 c) x c + a+b+c c =0 & c x^2+(b+2 c) x+(a+b+c)=0 aligned On comparing with p x^2+q x+r=0 , we get r=a+b+c

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