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If x 2 + ax + b = 0 and x 2 + bx + a = 0 have a common root, the value of (a + b) is

If x2 + ax + b = 0 and x2 + bx + a = 0 have a common root, the value of (a + b) is

Grade:11

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

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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