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For a polynomia g(x) with real coefficie...

For a polynomia g(x) with real coefficients, let `m_(g)` denote the number of distinct real roots of g(x). Suppose S is the set of polynomials with real coefficients defined by
`S={(x^(2)-1)^(2)(a_(0)+a_(1)+a_(2)x^(2)+a_(3)x^(3)): a_(0) a_(1), a_(2), a_(3)= RR}`
For a polynomial f. let f and f denote its first and second order derivties, respectively. Then the minimum possible value of `(m_(f')+m_(f"))`. where ` f in S` is, ____

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