Question

the degree of the polynomial graphed is 3. how many imaginary solutions does it have? 2 1 0 3 the degree tells you the number of real and imaginary solutions a polynomial function has. if it has a degree of 3, that means it has 3 solutions. how many real solutions are showing on the graph? the rest of its solutions have to be imaginary.

Explanation:

Step1: Count real - solutions

The number of real solutions of a polynomial is equal to the number of times the graph of the polynomial intersects the x - axis. From the graph, the polynomial intersects the x - axis at 1 point.

Step2: Use the degree - solution relationship

The degree of the polynomial is 3. The total number of real and imaginary solutions of a polynomial is equal to its degree. Let the number of real solutions be $r$ and the number of imaginary solutions be $i$. We know that $r + i=3$. Since $r = 1$, then $i=3 - r$.

Step3: Calculate the number of imaginary solutions

Substitute $r = 1$ into the equation $i = 3 - r$. So $i=3 - 1=2$.

Answer:

2