If has only 2 real roots, which of the following is true? A. b=-2a B. b>-2a C. b<2a D. b<-2a E. none of them above.

Can someone pls explain how to solve this? Thanks in advance~

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- Aug 3rd 2012, 07:38 AMshiny718Polynomial of degree 4 with 2 real roots
If has only 2 real roots, which of the following is true? A. b=-2a B. b>-2a C. b<2a D. b<-2a E. none of them above.

Can someone pls explain how to solve this? Thanks in advance~ - Aug 3rd 2012, 08:21 AMProve ItRe: Polynomial of degree 4 with 2 real roots
- Aug 3rd 2012, 08:23 AMDevenoRe: Polynomial of degree 4 with 2 real roots
if has but 2 real roots, then must have but 1 real root, so its discriminant:

since we have that:

EDIT: upon further reflection, and seeing ProveIt's answer, it's clear that although this condition is necessary, it is not sufficient, because u must be non-negative for x to be real.

this means that u = -(2a+b)/2a when Δ = 0. unfortunately, if we do not know if a > 0, we cannot decide if we should have 2a+b > 0, or 2a+b < 0.

one thing is certain, however, if b = -2a, then we only have one root for x.