Recent content by zero1207

I think I see what you're saying, a and c can't be integers for their product to be 11, but they could both be rationals. I'm trying to prove that the polynomial is irreducible over Q. I do see that when I put b(-b^2+7)=11 into a calculator, my solution is not a rational number. That...

I've also tried breaking up the polynomial into two smaller ones: x^3-7x+11=(x+a)(x^2+bx+c)=x^3+(a+b)x^2+(ab+c)x+ac so from this, I get: a+b=0; ab+c=-7; ac=11 by rearranging the equations I get b(-b^2+7)=11, but I don't know where I could go from there to show that no solutions for b exist in Q.

Homework Statement Prove that f(x)=x^3-7x+11 is irreducible over Q Homework Equations The Attempt at a Solution I've tried using the eisenstein criterion for the polynomial. It doesn't work as it is written so I created a new polynomial...

Ok, maybe I'm missing some obvious thing but does the information you gave let me calculate dx/dt? I'm still confused. I was pretty sure I'd use that information after I had calculated the differential equation.

Sorry I didn't post what work I've tried: if x(t) is amount of salt in that tank then dx/dt=Volume in*Salt Concentration in-Volume out*Salt Contentration out dx/dt=Volume in*(0)-Volume Out*(x/500) dx/dt=-(x/500)*(Volume Out)

I haven't found any examples anywhere on how to do a mixing problem where you don't know the rate of volume change, could someone give me a hand just setting up the equation? Here is the problem. . . [b]1. A tank contains 500 gal of a salt-water solution containing 0.05 lb of salt per gallon...