This Is Why I Hate Beetroot

Algebra Level 5

Consider the quartic equation :
x4+ax3+bx2+cx+d=0 x^4+ax^3+bx^2+cx+d = 0

If the sum of the first two roots of the equation is equal to the sum of the last two roots, then find the range of values of c\displaystyle c, such that, b+c=1\displaystyle b+c = 1 and a2a\neq -2

Details and Assumptions:
\bullet The roots may also be complex.
\bullet a,b,c,d a,b,c,d are real numbers.

Image credit: National Cancer Institute
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