Need a little help with biquadratic equations

[Noiro]

Homework Statement

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.

Homework Equations

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

 

[Mark44]

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.

 

[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.