Write the equation in standard form of the polynomial that has zeros at x=±6i

Step-by-step explanation:

We want to find the equation in standard form for a polynomial that has zeros at x=6i and x=-6i.  

So, we will have the two factors:

So, our polynomial will be:

Distribute:

Distribute:

Combine like terms:

Remember that i²=-1. Hence:

Simplify. So, our polynomial is:

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c