# This Is Why I Hate Beetroot

Algebra Level 5

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

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.

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