Polynomial Min Value: Find a & b Real #s

[VertexOperator]

Then how do I find the discriminant of the quartic equation? Do I even need the discriminant?

 

[Dick]

Then how do I find the discriminant of the quartic equation? Do I even need the discriminant?

No, you don't need any kind of discriminant. If you have one real root, say r, it turns out there aren't many possiblities for the value of that root. Look around at past posts and see if you can find a fact that can help you prove that.

 

[epenguin]

When I assume we have one real root of multiplicity 2 I get a^2=-4(b+2), is that right?

Then how do I find the discriminant of the quartic equation? Do I even need the discriminant?

That was explained and discussed in #22. Your equation is quite related to my expression there, but they are not in agreement so one of us has made a mistake.

Necessary? It is one way, worth pursuing in a complete job, but you have also been pointed to another way starting from conditions that give a double root.