SOLUTION: A polynomial with real coefficients has 3, 2i, and –i as three of its zeros. What is the least possible degree of the polynomial?
a. 3
b. 4
c. 5
d. 6
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-> SOLUTION: A polynomial with real coefficients has 3, 2i, and –i as three of its zeros. What is the least possible degree of the polynomial?
a. 3
b. 4
c. 5
d. 6
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Question 986485: A polynomial with real coefficients has 3, 2i, and –i as three of its zeros. What is the least possible degree of the polynomial?
a. 3
b. 4
c. 5
d. 6 Answer by solver91311(24713) (Show Source):
According to the Fundamental Theorem of Algebra, the number of zeros of a polynomial function is equal to the degree of the function.
Rational zeros can be singular, but irrational and complex zeros always appear as conjugate pairs. Hence if is a zero, even if the value of the real part is zero, then the conjugate, , must be a zero as well.
You were given one rational zero and two complex zeros that are NOT conjugates of each other. So how many do you count?
John
My calculator said it, I believe it, that settles it
