I need to use the given root to find the solution set of the polynomial equation?

Too much working. Let a, b, c and d be roots. Given a = 2i, means b=-2i abcd = 24, and ab = 4, so cd = 6 a+b+c+d = 1, and a+b = 0, so c+d=1 So c = 1/2 + ig and d = 1/2 - ig.

Cd = 1/4 + g² = 6, so g² = 23/4, so g =?23/2 and hence the roots are 2i, -2i, 1/2 + i?23/2, and 1/2 - i?23/2.

If 2i is a root then -2i is also a root (x - 2i)(x + 2i) = x^2 + 4 is a factor of the polynomial divide to get another quadratic: x^2 - x + 6 = 0 Use the quadratic formula: x = 1 +- sqrt(1 - 4(1)(6))/2 = 1 +- sqrt(-23)/2 x = 1/2 +- sqrt(23)i and x = 2i, - 2i.

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