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Find a 3rd degree polynomial with roots 6 and -i with constant coefficient -24.
A. f(x)=4x^3-24x^2+24x-24
B. f(x)=4x^3-24x^2+4x-24
C. f(x)=x^3-6x^2+x-24
D. f(x)=-4x^3+24x^2+4x-24
E. None of the above
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Under the given conditions, the roots of the polynomial should be 6, +i and -i.
Let us check the polynomial B.
f(x) = = + =
= + = .
Now you can see that this factored polynomial satisfies to the given condition.
So, the option B is good.
For the polynomials A) and C) the number 6 is not the root.
For the polynomial D) the number i is not the root.
So, the answer is the only option B.