SOLUTION: Suppose a polynomial function of degree 4 with rational coefficients has the following given numbers as zeros. Find the other​ zero(s).
i, 7 square root of 11
Algebra.Com
Question 1095091: Suppose a polynomial function of degree 4 with rational coefficients has the following given numbers as zeros. Find the other zero(s).
i, 7 square root of 11
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
If a polynomial has rational coefficients, then irrational and complex roots must occur in conjugate pairs.
In case you aren't familiar with the term conjugate pairs, the conjugate of the complex number a+bi is a-bi; the conjugate of the irrational number a+b*sqrt(c) is a-b*sqrt(c).
So in your example, with one root i, another root must be -i; and with one root 7*sqrt(11), another root must be -7*sqrt(11).
The four roots are the conjugate pairs
(1) i and -i
(2) 7*sqrt(11) and -7*sqrt(11)
RELATED QUESTIONS
a polynomial function of degree 4 with rational coefficients has the given numbers as... (answered by ikleyn)
suppose a polynomial function of degree 4 with rational coefficients has the following... (answered by Boreal)
Suppose a polynomial function of degree 5 with rational coefficients has given numbers as (answered by math-vortex,richwmiller)
Suppose a polynomial of degree 4 with rational coefficients has the given numbers as... (answered by josgarithmetic)
Suppose a polynomial function of degree 4 with rational coefficients has the given... (answered by solver91311)
find a polynomial function of lowest degree with rational coefficients that has the given (answered by tommyt3rd)
Find a polynomial function of lowest degree with rational coefficients that has the given (answered by Fombitz)
Suppose that a polynomial function of degree 4 with rational coefficients has... (answered by ikleyn)
Suppose that a polynomial function of degree 4 with rational coefficients has 6, 4, 5i as (answered by jim_thompson5910)