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julia-pushkina [17]
3 years ago
8

Which of the following is a polynomial with roots 2, 3i, and −3i? f(x) = x3 − 2x2 + 6x − 9 f(x) = x3 − 6x2 + 9x − 18 f(x) = x3 −

6x2 + 18x − 2 f(x) = x3 − 2x2 + 9x − 18
Mathematics
2 answers:
Andreas93 [3]3 years ago
4 0
F(x) = x3 − 2x2 + 9x − 18
vagabundo [1.1K]3 years ago
3 0

Answer:

f(x)=x^3-2 x^2+9 x-18

Step-by-step explanation:

The roots of the polynomial are 2,3i,-3i.

This implies that x-2,x-3i,x+3i are factors of the given polynomial.

The polynomial will have equation;

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

We expand using difference of two squares on the complex conjugates to get;

f(x)=(x-2)(x^2-(3i)^2)

\Rightarrow f(x)=(x-2)(x^2-(-3)^2(i)^2).

\Rightarrow f(x)=(x-2)(x^2-9(i)^2).

Recall that;

\boxed{i^2=-1}

\Rightarrow f(x)=(x-2)(x^2+9).

Expand using the distributive property to get;

\Rightarrow f(x)=x^3+9x-2x^2-18.

We rewrite in standard form to obtain;

f(x)=x^3-2x^2+9 x-18

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The value of the expression 4(5² - 3 - 2x)² is <u>576</u>.

In the question, we are asked to evaluate the expression 4(5² - 3 - 2x)², where x = 5.

To find the value of the expression, we find the value of each term with the value assigned to the variable and then put back the terms in the expression to get the final value.

The term 5² = 25.

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Taking the terms back to the expression, we get:

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Thus, the value of the expression 4(5² - 3 - 2x)² is <u>576</u>.

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