# This Is Why I Hate Beetroot

**Algebra**Level 5

Consider the quartic equation :

\[ x^4+ax^3+bx^2+cx+d = 0\]

\[ x^4+ax^3+bx^2+cx+d = 0\]

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 \(\displaystyle c\), 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.

###### Image credit: National Cancer Institute

**Your answer seems reasonable.**Find out if you're right!

Sign up to access problem solutions.

**That seems reasonable.**Find out if you're right!

Already have an account? Log in here.