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Select all factors given the roots: x={-3i,2,3.5} x^(2)-9 7x+2 x-2 7x-2 x+3.5 x^(2) x+14 2x+7 2x-7 x-14 x^(2)+9

User David E
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1 Answer

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Final answer:

Using the given roots {-3i, 2, 3.5}, the corresponding factors are (x²+9) for the pair of complex roots, (x-2) for the root 2, and (x-3.5) for the root 3.5. None of the other provided expressions match these roots.

Step-by-step explanation:

The student is asking to select all factors of a polynomial given its roots: {-3i, 2, 3.5}. When we have roots of a polynomial, the corresponding factors can be determined by writing the roots in the form of (x - root). For complex roots they come in conjugate pairs, so if -3i is a root, we would also have 3i as a root, and the corresponding factor would be x²+9. The root 2 would give us the factor (x-2), and the root 3.5 would give us the factor (x-3.5). None of the other expressions provided can be directly derived from the given roots.

User Justin Pollard
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