Help with polynomial of a given degree with given zeros.

label Algebra
account_circle Unassigned
schedule 1 Day
account_balance_wallet $5

Find a polynomial f(x) of degree 3 with real coefficients and the following zeros.

-1 , 2i

Simplify completely including i's.

Oct 17th, 2015

Hello!

If a polynomial has zero a, it can be expressed as (x-a)*(some other polynomial). Also, if a polynomial with real coefficients has a complex (non-real) root z, then the conjugate of z is also its root. Conjugate of 2i is -2i.

So, p(x) = a*(x+1)*(x-2i)*(x+2i) = a*(x+1)*(x^2+4) = a*(x^3+x^2+4x+4).
Here a is any real number except 0.

Please ask if something is unclear.
Oct 17th, 2015

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
Oct 17th, 2015
...
Oct 17th, 2015
Oct 19th, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer