How to factor this function?
y = x^4 + x^2 + 2
what is the solution to that integral?
here's what Wolfram spits out ...
http://www.wolframalpha.com/input/?i...Bx%5E2%2B2)+dx
$a+c=0 \implies a = -c$
$bc+ad=0 \implies bc - cd = 0 \implies c(b-d) = 0 \implies b = d$
$bd = 2 \implies b = d = \pm \sqrt{2}$
$b + ac+d = 1 \implies ac = 1-(b+d) \implies -c^2 = 1-(b+d) \implies c^2 = (b+d)-1 = 2b-1$ ... $c^2 > 0 \implies b=d=\sqrt{2}$ and $c = \pm \sqrt{2\sqrt{2}-1} \implies a=\mp \sqrt{2\sqrt{2}-1}$
$x^4+x^2+2 = (x^2 -\sqrt{2\sqrt{2}-1} x + \sqrt{2})(x^2 +\sqrt{2\sqrt{2}-1} x + \sqrt{2})$
any fourth degree polynomial with real coefficients and no real roots of the form
can be factored as follows ( real )
multply out to get
and compare coefficients and note that must be positive otherwise the polynomial has real roots