ohohaye
  • ohohaye
How many zeros does the function have over the set of complex numbers? Function: x^4+x^3-6x^2-14x-12=0
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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ParthKohli
  • ParthKohli
fundamental theorem of algebra
ParthKohli
  • ParthKohli
do you know that theorem?
denisaboichuk
  • denisaboichuk
just one

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More answers

ohohaye
  • ohohaye
Is it \[\frac{b \pm \sqrt{b ^{2}-4(a)(c)} }{ 2(a) }\]
ohohaye
  • ohohaye
@ParthKohli
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
  • ohohaye
oh...
ohohaye
  • ohohaye
Oops...
ParthKohli
  • ParthKohli
I think you can Google the theorem and it's just a second's work to find the number of complex solutions.
Astrophysics
  • Astrophysics
https://www.mathsisfun.com/algebra/fundamental-theorem-algebra.html
ohohaye
  • ohohaye
So it is where the graph passes the x-axis?
ohohaye
  • ohohaye
The roots are the zeros?
ohohaye
  • ohohaye
So are there 3 possible zeros/roots?
ganeshie8
  • ganeshie8
The peoblem is not about x intercepts. It is asking how many solutions are there to the given equation over complex numbers
ganeshie8
  • ganeshie8
|dw:1450163802033:dw|
ganeshie8
  • ganeshie8
Look at the given polynomial what is the degree ?
ohohaye
  • ohohaye
5
ganeshie8
  • ganeshie8
how did u get 5 ?
ohohaye
  • ohohaye
Do you mean on my problem?
ganeshie8
  • ganeshie8
Oh yes, your problem...
ohohaye
  • ohohaye
4
ganeshie8
  • ganeshie8
degree is 4, so there will be exactly 4 zeroes
ohohaye
  • ohohaye
Oh, so the leading degree is the amount of zeros?
ganeshie8
  • ganeshie8
Exactly! If the degree is 10, then there will be 10 zeroes
ganeshie8
  • ganeshie8
as simple as that
ganeshie8
  • ganeshie8
but you need to be careful, that count includes multiplicity of the zeroes too
ohohaye
  • ohohaye
That is when there are two numbers with the same degrees right?
ganeshie8
  • ganeshie8
Nope. consider below polynomial : \[p(x) = x^2-2x+1\]
ganeshie8
  • ganeshie8
In light of previous problem, can you tell the number of zeroes of above polynomial ?
ohohaye
  • ohohaye
Oh wait, I remember. That would be 3 because the 2x has an invisible 1 exponent right?
Astrophysics
  • Astrophysics
Note the degree!
ohohaye
  • ohohaye
its 2
ganeshie8
  • ganeshie8
right, so there will be exactly 2 zeroes
ganeshie8
  • ganeshie8
can you find them ?
ohohaye
  • ohohaye
x^2
ohohaye
  • ohohaye
Can you please just tell me
ganeshie8
  • 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
  • ganeshie8
Incase if you just want the answer for your actual problem, the answer is 4
ohohaye
  • ohohaye
ok, so the number at the end has a coefficient of 0 and those are considered complex numbers?
ganeshie8
  • ganeshie8
you're asking questions with different levels of difficulty... by any chance are you skipping lessons ?
Astrophysics
  • Astrophysics
The link I sent earlier has all this info
Astrophysics
  • Astrophysics
Maybe just read it, has examples to not too long either https://www.mathsisfun.com/algebra/fundamental-theorem-algebra.html
ganeshie8
  • 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
  • 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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