Tag Info

New answers tagged

4

This is an interesting question that is not solvable in one simple step. Let's take a look at the assumptions. Since we have a fourth-order polynomial with integer coefficients we expect that there might be only complex conjugate roots. Now we have: Times @@ (x - (x /. Solve[ x^4 - (2 m + 4) x^2 + (m - 2)^2 == 0, x])) (-Sqrt[2 - 2 Sqrt[2] Sqrt[m] + m] + ...


3

One simple approach is to try different values of m using the Factor function and check if the polynomials factor in the desired way. For example, contrast what happens when you have a polynomial that is simply factorizable such as Factor[x^4 - (2 m + 4) x^2 + (m - 2)^2 //. m -> 8] and what happens when you don't Factor[x^4 - (2 m + 4) x^2 + (m - 2)^2 ...


5

I'm not entirely sure what you are looking for. Do the factors need to have integer coefficients? If not, then you get a factorization into quadratics just by noting you have a polynomial in x^2 and hence can use the quadratic formula. The nonnegativity of both roots will follow, in this specific example, provided the discriminant is nonnegative. [Note: ...



Top 50 recent answers are included