Use the given zero to find all the zeros of the function. (Enter your answers as a comma-separated list. Include the given zero in your answer.)

Question

Function: 5x³+39x²+77x-17

Zero: -4 + i

x=

Answer 1

then -4 - i must also be a solution, ASSUMING the polynomial

has REAL coefficients, which it should!

then the factors are 0 = (x+4)+i and 0 = (x+4)-i

Multiplying them: [(x+4) + i] [ (x+4) - i ] =

[ (x+4)^2 + 1] =

[ x^2 + 8x + 16 + 1 ] =

x^2 + 8x + 17

is a factor

POlynomial long division:

5x -1

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x^2 + 8x + 17 | 5x^3 + 39x^2 + 77x - 17

5x^3 + 40x^2 +85x

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-x^2 - 8x - 17

-x^2 - 8x - 17

5x-1 is a factor, which means x = 1/5 is a solution

the solution set is { 1/5, -4 +or- i }