Form a polynomial, f(x), with real coefficients having the given degree and zeros.

Question

Degree: 4; zeros: 6i and 7i

I completely don't know what to do with this problem... if someone can solve and give a good explanation, I'd appreciate it.

Thanks.

Answer 1

Because the coefficients of f(x) are REAL,
f(x) has zeros: 6i and -6i, 7i and -7i.
For example,

f(x)=(x-6i)(x+6i)(x-7i)(x+7i)= (x^2+36)(x^2+49)