-Find a polynomial function of lowest degree with rational coefficients that has
ID: 2847092 • Letter: #
Question
-Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. -5i, 6
f(x)=...
-Find the rational zeros and then the other zeros for f(x)= 1/3x^3-1/4x^2-15/6x+47/192
The rational zeros are... and the other zeros are... (SEE BELOW)
-Use synthetic division to find P(k) for the given. k=2, P(x)=x^3-2x^2+7
P(2)=...
-Find a polynomial function of lowest degree with rational coefficients that has the given zeros 4-i, root5
f(x)=...
Find the rational zeros and then the other zeros for f(x). Select the correct choice below and fill in any answer boxes within The rational zeros are and the other zeros are .Explanation / Answer
COMPLEX ROOTS exist in conjugate pair
So,+5i will also be a root of the polynomial.
hence polynomial will be of min 3 degree having roots +5i,-5i & 6
So, polynomial is f(x)=(x-6)(x-5i)(x+5i)
=(x-6)(x^2+25)
=x^3-6x^2+25x-150.
other zeros are 1/4 - 3^0.5 & 1/4 + 3^0.5.
P(2)=8-8+7=7
f(x)=(x-5)(x-4+i)(x-4-i)
=(x-5)(x^2-8x+17)
=x^3-13x^2+57x-85.
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