Draw a picture of a polynomial with a degree of 4, that has a2 real zeros and 2 imaginary zeros.

Question

GUYS I REALLY NEED THIS SOONG I have been here for hours

Answer 1

Play around with this for a bit!

You need a degree of 4, so your best bet is to plan out a polynomial with four binomial factors, each with an x-term. Think of something like this:

(x + __)(x + __)(x + __)(x + __)

To have two real zeroes, give two of these binomials a real number to fill in the placeholder. Here's my example:

(x + 3)(x - 1)(x + __)(x + __)

To have two imaginary zeroes, give two of these binomials an imaginary quantity to fill in the placeholder. Here's my example:

(x + 3)(x - 1)(x + 4i)(x - 4i)

(Psst...have you ever wondered why you can factor (a² - b²) but not (a² + b²)? It's precisely because the latter gives complex roots when you factor it! Something to think about for this exercise. :) )

In its factored form, this is an example of a polynomial that can satisfy your description:

(x + 3)(x + 1)(x + 4i)(x - 4i)

If you need a polynomial in standard form, just multiply these terms together. You might need to use FOIL/distributive property a few times, and make sure you know how to multiply imaginary terms. If you need to convince yourself that my example or your own satisfies the requirements, check with a graphing calculator or online grapher such as Desmos. I hope this helps!