In equation `x^4-2x^3+4x^2+6x-21=0` if two of its roots are equal in magnitude but opposite in sign find the roots.

Explanation

Given that `alpha + beta = 0 but alpha + beta + gamma + delta = 2`. Hence ,
`gamma + delta = 2`
Let `alpha beta = p and gamma delta = q.` Therefore, given equation is equivelent to `(x^(2) + P)(x^(2) -2x + q) = 0`.
Comparing the coefficients, we get
`p + q = 4, -2p = 6 , pq = -21` .Therefore, p = -3, q = 7 and they satisfy pq = -21. Hence,
`(x^(2) - 3)(x^(2) - 2x + 7) = 0`
Therefore, the roots are `pm i sqrt(6)(where i = sqrt(-1))`