Question

PLEASE HELP!!!

Which of the following is a polynomial with roots -2, -3i, and 3i ?

a.) x3 + 4x2 + 9x + 24
b.) x3 - 4x2 + 9x - 24
c.) x3 + 2x2 + 9x + 18
d.) x3 - 2x2 + 9x - 18

Answer 1

synthetic division might be useful if you know it

Answer 2

or if you have a calculator, just plug in those values of x to see if they zero out

Answer 3

x3 + 4x2 + 9x + 24
0 -2 -4 -10
-2 | 1 2 5 [14] not zero, not a root

Answer 4

x3 - 4x2 + 9x - 24
0 -2 12 -42
-2 | 1 -6 21 (....) not zero, not a root

Answer 5

x3 + 2x2 + 9x + 18
0 -2 0 -18
-2 | 1 0 9 [0] is zero, so this ones a possible

x^2+9 has no real roots left in it, so its not this one

Answer 6

x3 - 2x2 + 9x - 18
0 -2 8 -18
-2 | 1 -4 17

hmmm, what am i mistyping

Answer 7

fine, lets try it this way

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

so nonr of them

Answer 8

(x+2)(x+3)(x-3)

x^2+3x+2x+6

(x^2+5x+6)(x-3)

x^3+5x^2+6x-3x^2-15x-18

x^3+2x^2-9x-18

Answer 9

That's weird. Like the poster above said, none of the choices work. Did you mistype it?

Answer 10

another way to do this question
Which of the following is a polynomial with roots -2, -3, and 3
means x= -2, x= -3 and x= 3
or (x+2)=0, (x+3)= 0, (x-3)=0
multiply together:
(x+2)(x+3)(x-3)=0
(x+3)(x-3) = x^2 -9

(x+2)(x^2-9) is x^3 + 2x^2 -9x -18

as noted above, none of your choices match this expression.
check for typos, and if you can't find a mistake, ask your teacher about this question.

Answer 11

@phi look at the question again.. sorry I forgot to put the "i"

Answer 12

ok then we start with
(x + 3i)(x-3i) = x^2 - 9i^2 = x^2 - 9(-1)= x^2 +9

now do
(x^2 +9)(x+2)= x^3 +2x^2 + 9x +18

Answer 13

notice I used
(x+y)(x-y) = x^2 + y^2 to expand (x + 3i)(x-3i)

also, used i*i = -1

Answer 14

okay?

Answer 15

The answer is choice c