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Question

The value of a+b if the equation x2+ax+b=0 and x2+bx+a=0 have a common root is

A
-1.0
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B
-1.00
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C
-1
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Solution

Let α be a common root of the equations.
Then α will satisfy the equations.
Thus,
α2+a.α+b=0(i)
α2+b.α+a=0(ii)
Subtracting the two equations, we get:
α(ab)+(ba)=0
α(ab)(ab)=0
α(ab)=(ab)
Since ab
α=1
Hence, placing the value of α in the equation (i), we get
12+a.1+b=0a+b=1
Hence, value of a+b=1


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