Prove that a polynomial P(x)X^4-3x^2+1 has exactly four radical.
how can i do it?
thanks.
I'm not sure if that's the correct way to go about it, but my 2 cents:
Using the quadratic formula, we get:
$\displaystyle x^2 = \dfrac{3 \pm \sqrt{9-4}}{2} = \dfrac{3 \pm \sqrt{5}}{2}$
Then, taking the square root;
$\displaystyle x = \pm\sqrt{\dfrac{3 \pm \sqrt{5}}{2}}$
Since all the roots in there are real, (the square root of 5 is less that 3) there must be 4 real roots.