what is the equation for k

Question

 is a degree 5 polynomial that passes through the origin, has zeros  and , and . Find the equation for .

Use  for your input. Simplify your answer so that it has only real numbers as coefficients.

Answer 1

So the roots are 0, i and -i, 7-i and 7+i

The polynomial factors as this:

a(x-0)(x-i)(x+i)(x-(7-i))(x-(7+i))

You will find a (leading coefficient) by plugin-in 1 and making it equal 370