If a, b, r, s are roots of x^4+x^3+x^2+x+3=0 Find value of (1+a)(1+b)(1+r)(1+s)

Question

If a, b, r, s are roots of x^4+x^3+x^2+x+3=0 Find value of (1+a)(1+b)(1+r)(1+s)
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Solution 1

The given equation is a quartic equation, and a, b, r, s are its roots. According to Vieta's formulas, the sum of the roots taken one at a time is -b/a, the sum of the roots taken two at a time is c/a, the sum of the roots taken three at a time is -d/a, and the product of the roots is -e/a.

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