Given complex zeros find the polynomial - Online Tutor

👉 Learn how to write the equation of a polynomial when given complex zeros. Recall that a polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a polynomial are the values of x for which the value of the polynomial is zero. Also recall that when a complex number is a zero to a polynomial, the conjugate of the complex number will also be a zero to the polynomial.

To write the equation of a polynomial, we write the given zeros in factor form and expand the product of the factors. Thus, given a, b, . . . as zeros to a polynomial, we write the equation of the polynomial by expanding the factors (x - a)(x - b) . . . = 0

Organized Videos:
✅Write the Equation of a Polynomial Given the Zeros
✅Write the Equation of a Polynomial Given Complex Zeros
✅Write the Equation of a Polynomial Given Zeros with Fractions
✅Write the Equation of a Polynomial Given Real Zeros
✅Write the Equation of a Polynomial Given Irrational Zeros
✅Write the Equation of a Polynomial Given Imaginary Zeros
✅Write the Equation of a Polynomial Given Zeros | Learn About

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[brianmclogan]

thank you I hate math videos on the paper, or even a computer, is it just me or does that make watching even more boring, I know I am not the most humorous person or most exiting but c'mon. Thanks for the love

[t.brookehaskett]

I'm a single mom of 4, back in school full-time and having to start over with my math classes. I literally have no idea how I would have survived the last two semesters without these videos. You rock the kasbah.

[camhdz]

God, these videos have literally been my salvation.

[illuminati]

Can't express my gratitude enough. You've helped me countless times. Thank you.

[tylerjohnson]

I don’t usually comment on videos (and I know that nobody will see this), but Mr. McLogan has become my primary teacher throughout Pre-Calc and Algebra 2. You have an incredible talent that so many of us rely on - and I know I can turn to you for any questions that I have!

Thank you!

[Brokentool_]

You're a hero. The college online math class I take provides "how to" without showing work or giving the steps it just gives you the question and the answer, it's an absolutely mockery of the education system.

[Maya-ubcb]

Thank you! We had a substitute teachee today, so we just watched a video on building polynomials. The video didn’t talk about imaginary numbers, so this is helping me so much with my homework. I have a quiz tomorrow which won’t impact my grade, but I was still super stressed because I didn’t understand.

[faisalalmuhawes]

Nowadays, during COVD19. We are taking are our exams at home. I have faced this trick in the middle of a problem, then I quickly searched about it here, and the problem is solved. If the exam is taken at college, I think I will lose about two grades. Thanks, Mr. Brian.

[TheAmandaAponte]

I have been working on the same problem for the past 4 hours. Nothing in my notes and no examples in the book for this type of problem! THANK YOU!!

[caroliner]

sal khan is NOTHING compared to this guy. you are the only reason why i’m passing math rn. you are amazing!

[Zandrake]

Thank you so much! This helped me out with my homework. I am unable to learn a whole lot in class from my teacher so I have to teach myself with the textbook and, of course, online resources. I'm glad you had exactly what I needed.

[katherine]

I WAS LOOKING EVERYWHERE FOR A VIDEO LIKE THIS! THANK YOU SO MUCH!

[joshnolan]

Just for the record, (I know this was posted in 2011, but my OCD won't let it go) in line 3, you should have written it as (x-2)((x-4)^2 –i^2). That extra parenthesis ensures that you distribute property. You somehow still managed to get the answer right. If you had missed the error and continued to do it without the parenthesis, your answer would incorrectly come out to x^3 –10x^2 +32x –31 as mine did at first.

[bhavikupadhyaya]

This man single caused me passing my exam today

[brianmclogan]

haha thanks, I am hoping the views will continue to increase as I work on organizing and tagging all of my videos I post.

[Celldweller]

what a king. I wouldn't be doing my homework without this man

[amruthaayyappan]

Thank you. Also I have a question, so when you’re doing x-(4-i) wouldn’t you distribute the negative??

[alieninstallation]

Thank you for these videos. One thing ive been struggling with and notice you didn't have a video on is when the zeros of a polynomial are given along with a CONSTANT. Multiply all the factors out and then at the end multiply the whole polynomial by whatever gets the end term to that constant?

[leonardmohr]

Awesome video, helps a bunch.  I think you made a mistake that confused me for a second, and just putting it here so others don't get confused like I did, but i believe you forgot to multiply +i and -i by -1 when you were regrouping so it should instead be regrouped as (x-2)((x-4)-i)((x-4)+i).  Doesn't actually make a difference in finding the correct answer :)

[cr]

Helped me a lot. Great video. My teacher left out much of the explanation because she assumed everyone knew it.

I especially like the way you write out the product of distribution, so that it isn't a single line and you have to discern like terms afterwards. I had never thought of doing that, and having tried it myself on a few problems, it is a lot clearer.