# Need a little help with biquadratic equations

1. Mar 17, 2009

### Noiro

1. The problem statement, all variables and given/known data

Ok, so here's the problem:
Prove, that biquadratic equation's x4+px2+q=0 sum of all solutions is equal to zero, and product is equal to q.

2. Relevant equations

3. The attempt at a solution
I don't really know how to solve it so I'd be very grateful if someone could help me. Thank you

2. Mar 17, 2009

### Staff: Mentor

This equation is quadratic in form, which you can see by letting u = x2. This makes the new equation u2 +pu + q = 0.
Solve that equation for u by using the quadratic formula, getting two values of u.
Replace u by x2, getting four values of x.

3. Mar 17, 2009

### Hogger

While that equation is quadratic in form, for the purpose of the question think of it as x4+ 0*x3+ px2 +0*x+q=0. Do you know any general ways to relate the coefficients of a polynomial with the roots? If you're having trouble try multiplying out (x-a)(x-b)(x-c)(x-d)=0. That will become a polynomial with roots equal to a,b,c, and d.