Answer:
The polynomial with roots 2, –3i, and 3i is:
\(x^3-2x^2+9x-18\)
Step-by-step explanation:
We are given three roots of a polynomial as:
2, -3i, 3i
Let p(x) be the polynomial whose roots are defined above.
Now we can find the equation of the polynomial as follows:
\(p(x)=(x-2)(x-3i)(x+3i)\\\\\\\i.e.\\\\\\p(x)=(x-2)(x^2-(3i)^2)\\\\\\p(x)=(x-2)(x^2-9i^2)\\\\\\p(x)=(x-2)(x^2+9)\\\\\\p(x)=x(x^2+9)-2(x^2+9)\\\\\\p(x)=x^3+9x-2x^2-18\\\\\\p(x)=x^3-2x^2+9x-18\)
Hence, the answer is: Option: D
The polynomial is: \(x^3-2x^2+9x-18\)
