Let the roots of the first equation be alpha and beta, giving their sum as alpha plus beta equals minus p and their product as alpha beta equals q. For the second equation with roots alpha to the fourth and beta to the fourth, the sum of roots r equals alpha to the fourth plus beta to the fourth. Expanding this sum yields two times q squared minus p squared times p squared minus 2q. Substituting this expansion for r in the target quadratic equation's discriminant, we get 16 times q squared minus 4 times q times two times q squared minus r, which simplifies to a negative value. Because the discriminant is positive but the product of the roots given by two times q squared minus r is negative, the roots are of opposite signs. Therefore, the roots are one negative and one positive.