Question

Using the given zero, find all other zeros of
f(x) -2i is a zero of f(x) = x4 - 5x2 - 36

Answer 1

f(x) has REAL coefficients, so what do we know about Complex Zeros?

Answer 2

Its hard to remember like I have the choices of

2i, 6i, -6i

2i, 3i, -3i

2i, 6, -6

2i, 3, -3

Answer 3

I am not interested in choices. I am interested in you learning.

Polynomials with REAL coefficients, if they have COMPLEX zeros, MUST have hose Complex zeros in "Conjugate" pairs. Are we ringing bells?

You have -2i, so there must be +2i

Personally, I'm tempted to use the quadratic formula:

\(x^{2} = \dfrac{5\pm\sqrt{25 + 4(36)}}{2} = \dfrac{5\pm\sqrt{169}}{2} = \dfrac{5\pm 13}{2} = 9\;or\;-4\)

Well, THAT looks pretty helpful, even if I am embarrassed that I didn't see the factorization: \((x^{2}-9)(x^{2}+4)\)

Answer 4

oh yess I remembering now cause isn't it with some specific formula to be able to get the answer like r^2

Answer 5

That was just factoring (or the very laborious quadratic formula).

Given \(A*Something^{2} + B*Something + C\), the quadratic formula will always give you \(Something = The\;Formula\). In this case, "Something" was \(x^{2}\)