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### Course: Algebra (all content)>Unit 10

Lesson 32: Finding zeros of polynomials

# Finding zeros of polynomials (1 of 2)

Sal finds all the zeros (which is the same as the roots) of p(x)=x⁵+9x³-2x³-18x=0..

## Want to join the conversation?

• What did Sal mean by imaginary zeros?
• Some quadratic factors have no real zeroes, because when solving for the roots, there might be a negative number under the radical. The only way to take the square root of negative numbers is with imaginary numbers, or complex numbers, which results in imaginary roots, or zeroes. They always come in conjugate pairs, since taking the square root has that + or - along with it.
• So why isn't x^2= -9 an answer? Like why can't the roots be imaginary numbers? My teacher said whatever degree the first x is raised is how many roots there are, so why isn't the answer this:
X= { 0, +- (square root of) 2, +- 3i?
• The imaginary roots aren't part of the answer in this video because Sal said he only wanted to find the real roots.
You're totally right about if the problem was finding all of the roots, 3i and -3i would be included in the answer.
• Since it is a 5th degree polynomial, wouldn't it have 5 roots?
• It does it has 3 real roots and 2 imaginary roots.
Sal didnt really solve for x^2=-9 if you do, you get +or - 3i that is 2 complex roots and 3 real roots.
• I'm lost where he changes the (x^2- 2) to a square number was it necessary and I also how he changed it. In total, I'm lost with that whole ending.
• I don't understand anything about what he is doing. How did Sal get x(x^4+9x^2-2x^2-18)=0? And how did he proceed to get the other answers?
• for x(x^4+9x^2-2x^2-18)=0, he factored an x out
after this, you can see, 9x^2 and -2x^2 are both 2nd degree terms
further, he factored the new terms to simplify the polynomial
after this he factorized (x^2-2) [@ ] and then equated it all with zero because that's when we get factors of a polynomial. if a*b*c*d=0 then atleast one or more terms would need to be 0 (ain't that right?). so he continued to equate each of them with zero and the ones that gave out a real value of x were valid zeroes
• At , how could Zeroes and Roots be the same things?
• Yes, as kubleeka said, they are synonyms They are also called solutions, answers,or x-intercepts.
• Why are imaginary square roots equal to zero?
(1 vote)
• Same reply as provided on your other question. It is not saying that the roots = 0. A root or a zero of a polynomial are the value(s) of X that cause the polynomial to = 0 (or make Y=0). It is an X-intercept. The root is the X-value, and zero is the Y-value. It is not saying that imaginary roots = 0.
• This is not a question. It is a statement. Put this in 2x speed and tell me whether you find it amusing or not.
• How do you graph polynomials?
• There are many different types of polynomials, so there are many different types of graphs.
But the most simple polynomial x^2+x, looks like a U centered at the origin.
Hope this helps! :)