8/09/2014 If i (=√-1) is a root of g(x) = 5x⁴ – 3x³ + ax² + bx – 7 then find the value of a and b.

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8/09/2014 Solution. If i is root of g(x), then -i is also a root.
Then g(i) = 0 and g(-i) = 0.

Substitute and solve the 2 equations simultaneously, keeping in mind, that:

i² = -1,

i³ = -i,

and i⁴ = 1.

Answer: a = -2, b = -3