Mathematics

15.06.2020 15:10

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Which of the following is a polynomial with roots 2, –3i, and 3i ? .options: a]

Which of the following is a polynomial with roots 2, –3i, and 3i ? .options:
a] x3 + 4x2 + 9x + 24

b] x3 – 4x2 + 9x – 24

c] x3 + 2x2 + 9x + 18

d] x3 – 2x2 + 9x – 18

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alowery89

4,4(10 marks)

Out of the following choices, x3 – 2x2 + 9x – 18 is a polynomial with roots 2,-3i, and 3i. The correct answer is D.

gl648809

4,4(47 marks)

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

skylar1315

4,6(60 marks)

2976 is the answer

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