Question

Which answer best describes the complex zeros of the polynomial function? f(x)=x3+x2+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 two real zeros and one nonreal zero. The graph of the function intersects the x-axis at exactly one location. The function has one real zero and two nonreal zeros. The graph of the function intersects the x-axis at exactly one location.

Answer 1

The polynomial function f(x)=x³+x²+10x+10 has one real zero and two nonreal zeros.

Step-by-step explanation:

The polynomial function f(x)=x³+x²+10x+10 has two real zeros and one nonreal zero.

To determine the number of real zeros, we can use the discriminant. The discriminant is calculated as b² - 4ac. In this case, the coefficients are a = 1, b = 1, and c = 10. The discriminant is 1² - 4(1)(10) = -39. Since the discriminant is negative, the quadratic formula will yield two complex solutions.

Since the function intersects the x-axis at exactly one location, we can conclude that there is one real zero and two nonreal zeros.

Answer 2

Just took the quiz and can confirm that the answer is indeed:

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

Hope I could help :)