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

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 }}} A. The function has three real zeros. The graph of the function       Log On


   



Question 1127898: Which answer best describes the complex zeros of the polynomial function?
+f%28x%29+=+x%5E3+%2B+x%5E2+%2B+10x+%2B+10+
A. The function has three real zeros. The graph of the function intersects the x-axis at exactly three locations.
B. The function has one real zero and two nonreal zeros. The graph of the function intersects the x-axis at exactly one location.
C. The function has one real zero and two nonreal zeros. The graph of the function intersects the x-axis at exactly two locations.
D. The function has two real zeros and one nonreal zero. The graph of the function intersects the x-axis at exactly one location.

Is B the correct answer?

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

Apply the grouping method to factor the polynomial


x%5E3+%2B+x%5E2+%2B+10x+%2B+10 = %28x%5E3+%2B+x%5E2%29 + %2810x+%2B+10%29 = x%5E2%2A%28x%2B1%29 + 10%2A%28x%2B1%29 = %28x%5E2%2B10%29%2A%28x%2B1%29.


It follows from this decomposition,  that the correct answer is B) and only B).