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find (1+r) (1+s) (1+t) (1+u )if r,s,t,y are the roots of f(x)=3x^4-x^3+2x^2+7x+2

 Feb 27, 2021
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Expanding \((1+r)(1+s)(1+t)(1+u)\), we get: \(rstu + (rst + rsu + rtu + stu) + (rs + rt + ru + st + su + tu) + (r + s + t + u) + 1\)

We can use Vieta's to get: \(rstu = 2/3, rst + rsu + rtu + stu = -7/3,  rs + rt + ru + st + su + tu = 2/3, r + s + t + u = 1/3\)

Adding, we get \(2/3 - 7/3 + 2/3 + 1/3 + 1 = 1/3\)

 Feb 27, 2021

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