Are you watching these Quadratic Equations closely?

Algebra Level 5

If the three equations ; \(x^{2}+ax+12=0\) , \(x^{2}+bx+15=0\) and \(x^{2}+(a+b)x+36=0\) have a common root .

Then find the sum of maximum value of \(a\) and minimum value of \(b\) .

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