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).

Approved