If the difference between the corresponding roots of the equations x^2 +ax+b=0 and x^2+bx+a=0 is the same , then find the value of a+b .

Answers (1)

Solution:   Let    alpha ,eta be the roots of x^2+ax+b=0

                   and   gamma ,delta  be the roots of  x^2+bx+a=0

    Then  given 

                                    alpha -eta =gamma -delta

        Rightarrow                        sqrta^2-4b=sqrtb^2-4a

        Rightarrow                       a^2-4b=b^2-4a

        Rightarrow                 (a^2-b^2)+4(a-b)=0Rightarrow (a-b)(a+b+4)=0

         ecause                 a-b
eq0

        	herefore                 (a+b+4)=0Rightarrow a+b=-4.

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