f(x) is a cubic polynomial x3+ax2+bx+c such that f(x)=0 has 3 distinct integral roots and f(g(x))=0 does not have real roots where g(x)=x2+2x-5,then minimum value of a+b+c is=? The solution given is as follows- Let roots be p,q,r such that p<q<r.Since g(x) can take values from [-6,inf.],p<= -7, q<= -8 and r<= -9. I didnt understand how they got this from the info that g(x) can take the specified values. Can anyone plz explain??You can also post any other method to solve the sum.
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