Cubic + Quadratic = Choked up with less

Algebra Level pending

Suppose a cubical polynomial \(x^{3} + p x^{2} + qx + 72\) such that it is divisible by \(x^{2} + ax+ b\) and \(x^{2} + bx+ a\) . Here a is not equal to b. And \(a,b,q,p\) are constants . Find sum of squares of the roots of cubic polynomial + \(a + b + ab + 72\)

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