# Where to Start?

Algebra Level 5

For a fixed pair of real numbers $$(b, c)$$ with $$b < 0$$, find the number of possible values of $$a$$ that will satisfy the following conditions:

The equation $${ x }^{ 4 }+{ ax }^{ 3 }+{ bx }^{ 2 }+cx+d=0$$ with $$a,b,c,d \in R$$ has roots $${ x }_{ 1 },{ x }_{ 2 },{ x }_{ 3 },{ x }_{ 4 }$$ such that $${ x }_{ 1 }+{ x }_{ 2 }={ x }_{ 3 }+{ x }_{ 4 }$$.

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