Question

Which answer best describes the complex zeros of the polynomial function? f(x)=x3+x2−8x−8

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

a

Explanation:

took the test

Answer 2

we are given

`f(x)=x^3+x^2-8x-8`

We can use Descarte's sign rule to find number of real roots

Positive real roots:

`f(x)=x^3+x^2-8x-8`

we can see that number of sign changes in this function is 1

so, number of positive real root =1

Negative real roots:

Firstly, we will find f(-x)

`f(-x)=(-x)^3+(-x)^2-8(-x)-8`

`f(-x)=-x^3+x^2+8x-8`

we can see that number of sign changes in this function is 2

so, number of negative real root =2

so, total number of real roots = number of positive real roots + number of negative real roots

total number of real roots =1+2

total number of real roots =3

Since, the degree of this polynomial is 3

so, maximum number of roots must be 3

We know that all roots are also called x-intercept because it crosses x-axis at that value

so, function will cross x-axis thrice

so, option-A.......Answer