Degree 3 polynomial with integer coefficients with zeros -2i and 7/5

Step-by-step explanation:

Polynomial Construction

A polynomial can be constructed by knowing its roots or zeros and the leading coefficient.

In our example, we have only two roots and no leading coefficient, thus the solution provided will be only one of the infinite possible solutions.

There is one imaginary solution x=-2i, we know it the polynomial has integer coefficients, then the imaginary roots come in conjugated pairs, meaning the other root must be x=+2i. Having completed all the roots, our polynomial is

Operating

We can discard the denominator since the roots of the polynomial will be the same with or without it, and we need the coefficients to be integer.

Operating

Rearranging

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)