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Home Q & A Board Science-Related Homework Help Mathematics
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Banana Banana
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11 years ago
Solve: x^3+9x^2+16x-6

I know the answer, but I want to learn how to get to that answer. Could someone show me the steps please? Any help is greatly appreciated. Slight Smile For reference, the answer is: {-3, -3-?11, -3+?11}
Alright, so it's a mix between using the rational root test, guessing or trial and error, and synthetic divison? Darn, I have a similar problem on my final exam, it's a lot of writing, but I think I'll be fine for this problem, thanks! Smiling Face with Open Mouth
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wrote...
#1
11 years ago
Gotta use the Rational Root Test, then use synthetic division.

God, I hate these problems
wrote...
#2
11 years ago
You can't use the quadratic formula, because the x³ means this is not quadratic.
wrote...
#3
11 years ago
Solving these kind of problems is not easy, generally what you need to do this assume x = ± 1, 2, 3 as a factor and then solve.

so that,

x^3 + 9x^2 + 16x - 6
= x^3 + 3x^2 + 6x^2 + 18x - 2x - 6
= x^2(x + 3) + 6x(x + 3) - 2(x + 3)
= (x + 3)(x^2 + 6x - 2)

if we equate the above expression with 0 we get:

(x + 3)(x^2 + 6x - 2) =  0

x = - 3 or x^2 + 6x - 2 = 0

x = -3 , - 3 - ?11, - 3 + ?11
wrote...
#4
11 years ago
(x+3)

x+3   x^3+9x^2+16x-6  x^2+6x-2
       -x^3+3x^2
--------------------
               6x^2+16x
            - 6x^2+ 18x
===========================
                          -2x-6
                       -(-2x-6)
                       ===========
                                0

a=1 b=6  c=-2

x=-6+/- sq rt 6^2-4(1)(-2)/ 2
x=-6+/- sq rt 36+8/ 2
x=-6+/- sq rt 44/ 2
x=-6+/- 2 sq rt 11/2

x=-3+ sq rt 11  -3 - sq rt 11  -3
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