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Questions in which polynomials (single or several variables) play a key role. It is typically important that this tag is combined with other tags; polynomials appear in very different contexts. Please, use at least one of the top-level tags, such as nt.number-theory, co.combinatorics, ac.commutative-algebra, in addition to it. Also, note the more specific tags for some special types of polynomials, e.g., orthogonal-polynomials, symmetric-polynomials.
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roots of a fourth degree polynomial function (Vieta) [closed]
Question
I am interested in the root of the polynomial function :
$x^4+(a+b+c+d-2)x^3+(ab+ac+ad+bc+bd+cd-2b-2c-a-d)x^2
+(abc+abd+acd+bcd-ab-ac-ad-2bc-bd-cd-a-d+b+c)x+
abcd-abc-bcd-ad+bc=0$
Under the r …