SOLUTION: 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+4

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 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+4      Log On


   



Question 1028848: 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

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
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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) = 4x%5E3-24x%5E2%2B4x-24 = %284x%5E3+-24x%5E2%29 + %284x-24%29 = 

= 4x%5E2%2A%28x-6%29 + 4%2A%28x-6%29 = 4%2A%28x%5E2%2B1%29%2A%28x-6%29.

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.