1. ## Polynomial Proof

Prove that a polynomial P(x)X^4-3x^2+1 has exactly four radical.

how can i do it?

thanks.

2. I'm not sure if that's the correct way to go about it, but my 2 cents:

Using the quadratic formula, we get:

$x^2 = \dfrac{3 \pm \sqrt{9-4}}{2} = \dfrac{3 \pm \sqrt{5}}{2}$

Then, taking the square root;

$x = \pm\sqrt{\dfrac{3 \pm \sqrt{5}}{2}}$

Since all the roots in there are real, (the square root of 5 is less that 3) there must be 4 real roots.

3. so what is the 4 real roots>?

4. Unknown008 exhibited them in post # 2. Just take ++, +-, -+, -- combinations of the signs, and you'll get all four roots.