Complex roots: Given that z = -3/2 + i*sqrt{11}/2 is a root of z^4 - 3z^3 - z^2 + kz + 40 = 0, find...

[annaanna]

Am I going about it the right way? I dont know what the next step should be

 

[annaanna]

also is advanced math the topic i should choose? it says after calculus but what level of calculus

 

[blamocur]

Am I going about it the right way? I dont know what the next step should be View attachment 37395

You seem to be on a right path.
You know the values of 'a' and 'b' -- can you finish, i.e. right explicit coefficients, for your quadratic polynomial?
What is the relation between your quadratic polynomial and the original quartic one?

 

[Dr.Peterson]

Am I going about it the right way? I dont know what the next step should be View attachment 37395

Once you write the actual coefficients of the quadratic (which are simple), the next step might be long division. That works for me.

also is advanced math the topic i should choose? it says after calculus but what level of calculus

I would just call this (advanced?) algebra, though the context might be something higher (complex variables?). What course are you taking?

The definition of "advanced math" is vague, and each of us might express it differently; I wouldn't worry about it.

 

[annaanna]

You seem to be on a right path.
You know the values of 'a' and 'b' -- can you finish, i.e. right explicit coefficients, for your quadratic polynomial?
What is the relation between your quadratic polynomial and the original quartic one?

I dont know I struggle with that cause if I were to replace the z in the original quartic one with a +bi suddenly there's no more z's unlike my quadratic one.. do i substitute in a+bi for the z in my quadratic one too? Also isn't it too early to be able to link the coefficients in my quadratic with the quartic.. Also it doesn't help me if i changed the [math]a^2~+b^2[/math] to the modulus of z right?

 

[annaanna]

Once you write the actual coefficients of the quadratic (which are simple), the next step might be long division. That works for me.

I would just call this (advanced?) algebra, though the context might be something higher (complex variables?). What course are you taking?

The definition of "advanced math" is vague, and each of us might express it differently; I wouldn't worry about it.

are the actual coefficients [math]z^2-3z+\frac{9}{4}+\frac{11}{4}.[/math] ? Am I this silly

 

[blamocur]

Am I this silly

Even sillier :

1. What is the value of [imath]a[/imath] ? How about [imath]-2a[/imath] ?
2. Do you have difficulty adding up the constants ?

Once you address the above just follow @Dr.Peterson's suggestions in post #4.

 

[annaanna]

Even sillier :

1. What is the value of [imath]a[/imath] ? How about [imath]-2a[/imath] ?
2. Do you have difficulty adding up the constants ?

Once you address the above just follow @Dr.Peterson's suggestions in post #4.

if you mean the 9/4 +11/4 no i left them there just to make sure it was clear what step i was doing haha, if you dont mean those then i really am silly cause I dont know. Isn't a=-3/2 and then -2a would be 3 right?? (edit: realised I wrote -3 instead of 3 my bad)

 

[Dr.Peterson]

are the actual coefficients [math]z^2-3z+\frac{9}{4}+\frac{11}{4}.[/math] ? Am I this silly

if you mean the 9/4 +11/4 no i left them there just to make sure it was clear what step i was doing haha, if you dont mean those then i really am silly cause I dont know. Isn't a=-3/2 and then -2a would be 3 right??

Yes, just add 9/4 + 11/4 to get the constant, and correct the -3 to 3.

You need momentum -- keep going, don't stop to ask at every step! (But do check the results of each step.)

 

[annaanna]

Yes, just add 9/4 + 11/4 to get the constant, and correct the -3 to 3.

You need momentum -- keep going, don't stop to ask at every step! (But do check the results of each step.)

I am slowly losing confidence in myself with these questions, but that's not the right attitude you're right! Thanks for the help

 

[blamocur]

I am slowly losing confidence

Don't! Making and correcting mistakes is the most effective way to learn. For learners not making mistakes usually means not working and not learning.