SOLUTION: find the simplest polynomial with the given zeros (make sure you use ALL zeros) 1, square root of 3, -4, -4

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: find the simplest polynomial with the given zeros (make sure you use ALL zeros) 1, square root of 3, -4, -4      Log On


   

Question 1023217: find the simplest polynomial with the given zeros (make sure you use ALL zeros)
1, square root of 3, -4, -4
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
If the coefficients do not need to be integers, then:

f%28x%29=%28x-1%29%28x-sqrt%283%29%29%28x%2B4%29%28x%2B4%29

Multiply that out and get:



However if the coefficients must be integers then you
must include the conjugate of sqrt%283%29 also as a
zero and which is -sqrt%283%29.

Then 

f%28x%29=%28x-1%29%28x-sqrt%283%29%29%28x%2Bsqrt%283%29%29%28x%2B4%29%28x%2B4%29

Multiply that out and get:

f%28x%29=x%5E5%2B7x%5E4%2B5x%5E3-37x%5E2-24x%2B48

Edwin