



 
Hi Dave, Your graph may indicate there are no real roots but there are complex roots. Lets look at a quadratic first. If a quadratic has roots s and t (whether real or complex) then it can be written
Expansion gives
Hence the coefficient of x is minus the sum of the roots. Hence , for example for the quadratic equation x^{2} + 2x + 5 = 0 the sum of the roots is 2. What about a quartic? If a quartic equation has roots s, t, u and v then he quartic can be written
Expand this. Where do you see s + t + u + v? I hope this helps,  


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