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If x2 + ax + b = 0 and x2 + bx + a = 0 have a common root, the value of (a + b) is
Hi Ranjita,
Let x = p, be the common root of both the equations.
So p^2+ap+b=0, and
p^2+bp+a=0.
Subtract the two: we will get
p(a-b)+(b-a)=0 or (a-b)(p-1)=0.
If a=b, then the two equations will be one and the same and both the roots will be the same. So a≠b. Hence (p-1)=0 or p=1.
So substitute p=1 in any of the equation and we have
1+a+b=0 or a+b = -1.
Best Regards,
Ashwin (IIT Madras).
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