Practice!

Sample Problem

If g(x)=2x4-x3+49x2-25x-25 and one of the zeros of g(x) is -5i, what are all the other

three zeros of the function (in addition to -5i)?

Solution

Because we know that -5i is a zero and the polynomial has to have real coefficients,

we know that the conjugate 5i must also be a zero.

Multiplying these two known factors (x-5i)(x+5i)=x2+25. Using long division,

 divide x2+25 into the original function 2x4-x3+49x2-25x-25 to get 2x2-x-1.

2x4-x3+49x2-25x-25=(x2+25)(2x2-x-1)=(x-5i)(x+5i)(2x+1)(x-1)

Therefore the other zeros are 5i, -1/2, and 1.