If x^4 + x^3 + x^2 + x + 1 = 0 what is the value of the product (x1 + 1)(x2 + 1)(x3 +1)(x4 + 1) ?

Expert Answers

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f(x) = x^4 + x^3 + x^2 + x + 1

Usind Viete's rule:

x1+x2+x3+x4 = -b/a = -1

x1*x2+ x1*x3 + x1*x4 + x2*x3 + x3*x4 = 1

x1*x2*x3 + x1*x3*x4 + x2*x3*x4 = -1

x1*x2*x3*x4 = 1

let P = (x1+1)(x2+1)(x3+1)(x4+1) = x1+x2+x3+x4 +(x1x2+x1x3+x2x4+x2x3+x3x4) +x1x2x3x4 +x1x2x3+x2x3x4+x1x3x4+1

= -1 + 1 -1 + 1 + 1 = 1

Then: P = 1

Approved by eNotes Editorial Team
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