How many zeros does the function have over the set of complex numbers?
Function: x^4+x^3-6x^2-14x-12=0

- ohohaye

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- ParthKohli

fundamental theorem of algebra

- ParthKohli

do you know that theorem?

- denisaboichuk

just one

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## More answers

- ohohaye

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

- ohohaye

@ParthKohli

- ParthKohli

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

- ohohaye

oh...

- ohohaye

Oops...

- ParthKohli

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

- Astrophysics

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

- ohohaye

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

- ohohaye

The roots are the zeros?

- ohohaye

So are there 3 possible zeros/roots?

- ganeshie8

The peoblem is not about x intercepts.
It is asking how many solutions are there to the given equation over complex numbers

- ganeshie8

|dw:1450163802033:dw|

- ganeshie8

Look at the given polynomial
what is the degree ?

- ohohaye

5

- ganeshie8

how did u get 5 ?

- ohohaye

Do you mean on my problem?

- ganeshie8

Oh yes, your problem...

- ohohaye

4

- ganeshie8

degree is 4, so there will be exactly 4 zeroes

- ohohaye

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

- ganeshie8

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

- ganeshie8

as simple as that

- ganeshie8

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

- ohohaye

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

- ganeshie8

Nope. consider below polynomial :
\[p(x) = x^2-2x+1\]

- ganeshie8

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

- ohohaye

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

- Astrophysics

Note the degree!

- ohohaye

its 2

- ganeshie8

right, so there will be exactly 2 zeroes

- ganeshie8

can you find them ?

- ohohaye

x^2

- ohohaye

Can you please just tell me

- ganeshie8

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

- ganeshie8

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

- ohohaye

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

- ganeshie8

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

- Astrophysics

The link I sent earlier has all this info

- Astrophysics

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

- ganeshie8

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

- ohohaye

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

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