SOLUTION: Which answer best describes the complex zeros of the polynomial function? f(x)=x^3+x^2+10x+10 The function has three real zeros. The graph of the function intersects t

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Which answer best describes the complex zeros of the polynomial function? f(x)=x^3+x^2+10x+10 The function has three real zeros. The graph of the function intersects t      Log On


   

Question 1124416: Which answer best describes the complex zeros of the polynomial function?
f(x)=x^3+x^2+10x+10


The function has three real zeros. The graph of the function intersects the x-axis at exactly three locations.

The function has one real zero and two nonreal zeros. The graph of the function intersects the x-axis at exactly two locations.

The function has one real zero and two nonreal zeros. The graph of the function intersects the x-axis at exactly one location.

The function has two real zeros and one nonreal zero. The graph of the function intersects the x-axis at exactly one location.
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
x^3 + x^2 + 10x + 10 = (factorize; start grouping) = 


= (x^3 + x^2) + (10x + 10) = x^2*(x+1) + 10*(x+1) = (x^2 + 10)*(x+1).


The polynomial has one real root x= -1.


The answer is the choice line #3.

Solved.