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Question

If the difference between the corresponding roots of the equations x2+ax+b=0 and x2+bx+b=0(ab) is the same; then -(a+b)=.............

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Solution

αβ=(α+β)24αβ
For equation x2+ax+b=0-------(1)
Sum=a,Product=b
For equation x2+bx+b=0---------(2)
Sum=b,Product=b
For equation (1) ------Difference=a24b
For equation (2) ------Difference=b24b
Now a24b=b24b
a2b2=0
(ab)(a+b)=0
a+b=0 can be one of the solutions

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