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[SOLVED] Polynomial inequality
Show [tex]x^4-3x^3+4x^2-3x+1 \geq 0[/tex] for all real x.
[tex]a^2 \geq 0[/tex]
Cant think of any more.
I've tried to factor it relentlessly, because I would have sworn on my life there was a nice trick for factoring polynomials with symmetrical and alternating co efficients, but I can't remember...By observation i can see the inequality is trivial if x is less than 0 or greater than 3. But I can't fill the gap.
Homework Statement
Show [tex]x^4-3x^3+4x^2-3x+1 \geq 0[/tex] for all real x.
Homework Equations
[tex]a^2 \geq 0[/tex]
Cant think of any more.
The Attempt at a Solution
I've tried to factor it relentlessly, because I would have sworn on my life there was a nice trick for factoring polynomials with symmetrical and alternating co efficients, but I can't remember...By observation i can see the inequality is trivial if x is less than 0 or greater than 3. But I can't fill the gap.