Question

Writing Polynomial Functions from Complex Roots

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Which polynomial function has a leading coefficient of 3 and roots -4, i, and 2, all with multiplicity 1?
O f(x) = 3(x + 4)(x - 1)(x-2)
Of(x)=(x-3)(x + 4)(x-1)(x-2)
Of(x)=(x-3)(x + 4)(x - 1)(x + 1)(x - 2)
Of(x) = 3(x + 4)(x - 1)(x + 1)(x-2)
1
2
7

Answer 1

The polynomial function with a leading coefficient of 3 and roots -4, i, and 2, all with multiplicity 1 is f(x) = 3(x^2 + (2-i)x - 8 + 4i).

Step-by-step explanation:

The polynomial function with a leading coefficient of 3 and roots -4, i, and 2, all with multiplicity 1, can be written as:

f(x) = 3(x + 4)(x - i)(x - 2)

To simplify further, we can multiply the factors:

f(x) = 3(x^2 + 4x - ix - 4i)(x - 2)

Combining like terms, we get:

f(x) = 3(x^2 + 4x - ix - 2x - 8 + 4i)

Finally, simplifying the expression:

f(x) = 3(x^2 + 2x +(-i)x - 8 + 4i)

f(x) = 3(x^2 + (2-i)x - 8 + 4i)

So, the correct polynomial function is f(x) = 3(x^2 + (2-i)x - 8 + 4i).

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