SOLVING EQUATIONS WITH THE GIVEN ROOTS

Problem 1 :

ix3 + 2x2 + 1 = 0

If i is one root of the above equation, find the other roots.

Solution :

Problem 2 :

x4 - 2x2 - 3 = 0

If -√3 and √3 are the two roots of the above equation, find the other roots.

Solution :

Problem 3 :

x3 + 2x2 + 9x + 18 = 0

If 3i one root of the above equation, find the other roots.

Solution :

Problem 4 :

x- 4x3 + 4x2 + 36x - 117 = 0

If (2 + 3i) is one root of the above equation, find the other roots.

Solution :

Problem 5 :

Show that 2a is a root to the equation given below.

x3 + (4 - a)x2 - 2(2a + a2)x = 8a2

Solution :

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