This Is Why I Hate Beetroot
\[ x^4+ax^3+bx^2+cx+d = 0\]
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 \(\displaystyle c\), such that, \(\displaystyle b+c = 1\) and \(a\neq -2\)
Details and Assumptions:
\(\bullet\) The roots may also be complex.
\(\bullet\) \( a,b,c,d\) are real numbers.