ROOTS!

[keeyla]

Hi! I am doing math 11 and I am having trouble with roots. I have a horrible book to learn from!!!!!!!!!! Anyways this is the question.

What is the greatest number of roots each equation could have?
x[sup:11d0a807]3[/sup:11d0a807]+5x[sup:11d0a807]2[/sup:11d0a807]-6x-3=0

I don't understand what roots are. I have tried to find out but my book doesn't explain what they are. I am really frustrated. I have tried to move on from this question but I can't because I need to know what a root is. I have a billion more questions but I will just start here first.
I hope someone can help!
Thanks!

 

[Deleted member 4993]

Hi! I am doing math 11 and I am having trouble with roots. I have a horrible book to learn from!!!!!!!!!! Anyways this is the question.

What is the greatest number of roots each equation could have?
x[sup:2jxqetww]3[/sup:2jxqetww]+5x[sup:2jxqetww]2[/sup:2jxqetww]-6x-3=0

I don't understand what roots are. I have tried to find out but my book doesn't explain what they are. I am really frustrated. I have tried to move on from this question but I can't because I need to know what a root is. I have a billion more questions but I will just start here first.
I hope someone can help!
Thanks!

A polynomial of degree "n" will have - "n" roots (real and/or complex).

If you do not know what a "degree of polynomial" is - do a google search.

Then answer the question - What is the greatest number of roots the given polynomial can have?

Then answer the question - what is the degree of the given polynomial?

 

[wjm11]

What is the greatest number of roots each equation could have?
x^3+5x^2-6x-3=0

I don't understand what roots are.

Roots are just solutions to the equation. In other words, they are just all the values of x that would make this polynomial equal 0.

Here is another way of looking at it: If we change the 0 to y, we have y = x^3+5x^2-6x-3. If we graph this, every place the curve crosses the x-axis is called a "real" root ( in the domain of Real Numbers). The x values where the curve crosses the axis are the solutions to your equation.

Since this is a third order equation (the highest exponent on the variable x is 3), there are at most 3 real roots.

I don't know if your class has discussed imaginary/complex roots, so I won't go in to that too much. I'll just say that a third order equation can have 3 real roots or 1 real and 2 imaginary/complex roots.

Hope that helps.

 

[keeyla]

What is the greatest number of roots each equation could have?
x^3+5x^2-6x-3=0

I don't understand what roots are.

Roots are just solutions to the equation. In other words, they are just all the values of x that would make this polynomial equal 0.

Here is another way of looking at it: If we change the 0 to y, we have y = x^3+5x^2-6x-3. If we graph this, every place the curve crosses the x-axis is called a "real" root ( in the domain of Real Numbers). The x values where the curve crosses the axis are the solutions to your equation.

Since this is a third order equation (the highest exponent on the variable x is 3), there are at most 3 real roots.

I don't know if your class has discussed imaginary/complex roots, so I won't go in to that too much. I'll just say that a third order equation can have 3 real roots or 1 real and 2 imaginary/complex roots.

Hope that helps.

I just wanted to say thank you so much! I am not in a class learning this. I am learning this on my own out of a book. Math isn't my strong point so I find it difficult sometimes. Especially when the book leaves out vital information. I once again thank you and hope you can answer my other billion and one questions.

Kayla

 

[Denis]

.... and hope you can answer my other billion and one questions.

Didn't you say a billion only previously? :shock:

 

[keeyla]

Yes, but I already have more questions! lol