Question

How many zeros does the function have over the set of complex numbers?

Function: x^4+x^3-6x^2-14x-12=0

Answer 1

fundamental theorem of algebra

Answer 2

do you know that theorem?

Answer 3

just one

Answer 4

Is it \[\frac{b \pm \sqrt{b ^{2}-4(a)(c)} }{ 2(a) }\]

Answer 5

@ParthKohli

Answer 6

hehe no...
this is not a quadratic equation
the quadratic formula is a little wrong
the fundamental theorem of algebra is not even remotely close

Answer 7

oh...

Answer 8

Oops...

Answer 9

I think you can Google the theorem and it's just a second's work to find the number of complex solutions.

Answer 10

https://www.mathsisfun.com/algebra/fundamental-theorem-algebra.html

Answer 11

So it is where the graph passes the x-axis?

Answer 12

The roots are the zeros?

Answer 13

So are there 3 possible zeros/roots?

Answer 14

The peoblem is not about x intercepts.

It is asking how many solutions are there to the given equation over complex numbers

Answer 15

Look at the given polynomial
what is the degree ?

Answer 16

5

Answer 17

how did u get 5 ?

Answer 18

Do you mean on my problem?

Answer 19

Oh yes, your problem...

Answer 20

4

Answer 21

degree is 4, so there will be exactly 4 zeroes

Answer 22

Oh, so the leading degree is the amount of zeros?

Answer 23

Exactly!

If the degree is 10, then there will be 10 zeroes

Answer 24

as simple as that

Answer 25

but you need to be careful, that count includes multiplicity of the zeroes too

Answer 26

That is when there are two numbers with the same degrees right?

Answer 27

Nope. consider below polynomial :

\[p(x) = x^2-2x+1\]

Answer 28

In light of previous problem, can you tell the number of zeroes of above polynomial ?

Answer 29

Oh wait, I remember. That would be 3 because the 2x has an invisible 1 exponent right?

Answer 30

Note the degree!

Answer 31

its 2

Answer 32

right, so there will be exactly 2 zeroes

Answer 33

can you find them ?

Answer 34

x^2

Answer 35

Can you please just tell me

Answer 36

I suggest you watch this quick video first
https://www.khanacademy.org/math/algebra-basics/quadratics-polynomials-topic/polynomial-basics-core-algebra/v/terms-coefficients-and-exponents-in-a-polynomial

Answer 37

Incase if you just want the answer for your actual problem, the answer is 4

Answer 38

ok, so the number at the end has a coefficient of 0 and those are considered complex numbers?

Answer 39

you're asking questions with different levels of difficulty...
by any chance are you skipping lessons ?

Answer 40

The link I sent earlier has all this info

Answer 41

Maybe just read it, has examples to not too long either https://www.mathsisfun.com/algebra/fundamental-theorem-algebra.html

Answer 42

its not wise to attempt homework with out reading the required material
i can help you if you have a specific question... start somewhere :)

Answer 43

This is material that I went over at the beginning of the year and I forgot how to do it