Question

State how many imaginary and real zeros the function has.

f(x) = x^3 + 5x^2 + x + 5
Answer choices:0 imaginary; 3 real

1 imaginary; 2 real

3 imaginary; 0 real

2 imaginary; 1 real

Answer 1

there are no positive roots, since all the coefficients are positive
we can use descartes rule of sign to see how many negative ones there may be
or we could just solve it

Answer 2

1 imaginary; 2 real
3 imaginary; 0 real

these two choices are out, because imaginary roots come in conjugate pairs, so there must be an even number of them

Answer 3

turns out that this one has only one real root
how you are supposed to know that by looking at it i am not sure

Answer 4

so its 1 real and 2 imaginary? how would you get that?

Answer 5

i graphed it
http://www.wolframalpha.com/input/?i=+x^3+%2B+5x^2+%2B+x+%2B+5+
i guess the method would depend on what class you are taking

Answer 6

oh thank you! and precalculus!

Answer 7

ok, then i am not sure what method you are supposed to use
there are only two possibilities in your list, but i am not sure how to choose between them without a graph