Question 678441
If 7i and -7i are solutions then (x-7i) and (x-(-7i)) are factors. So we can start our equation with:
k(x-7i)(x-(-7i)) = 0
where "k" is any non-zero number. The last factor simplifies:
k(x-7i)(x+7i) = 0
Now we multiply the last two factors. We can use FOIL or the {{{(a-b)(a+b) = a^2-b^2}}} pattern. (I prefer using the pattern.)
{{{k((x)^2 - (7i)^2) = 0}}}
Simplifying...
{{{k(x^2 - 49i^2) = 0}}}
Since {{{i^2 = -1}}}:
{{{k(x^2 - 49(-1)) = 0}}}
{{{k(x^2 + 49) = 0}}}
Last of all, pick a value for k. It can be any non-zero number. (This is why the problem says "Write a equation..." instead of "Write the equation ...".) Picking a 1 for k makes things simple. Once you have your number for "k" just multiply out the left side using the Distributive Property.