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If the roots of x^2+2ax+b=0 differ from the root x^2+2bx+a=0 by a constant

If the roots of x^2+2ax+b=0 differ from the root x^2+2bx+a=0 by a constant .then a+b=

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A)
Let the roots of x^2+2ax+b=0 be p and q and that of x^2+bx+a = 0 be p and r

For the first equation, p+q = -a and pq = b and for the second equation p+r = -b and pr = a

therefore q = (b/a)r

Substituting this we get

p+(b/a)r = -a and p+r = -b, on subtracting both the equations we get, r = a and q = b

p+q = -a, that is p+b = -a, therefore p = -(a+b) or a+b = -p
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