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The "cubic" $x^3+2x^2-11x-12$ has three roots. What is their sum?

Guest Dec 30, 2017
 #1
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+1

Solve for x:

x^3 + 2 x^2 - 11 x - 12 = 0

 

Factor the left hand side.

The left hand side factors into a product with three terms:

(x - 3) (x + 1) (x + 4) = 0

 

Find the roots of each term in the product separately.

Split into three equations:

x - 3 = 0 or x + 1 = 0 or x + 4 = 0

 

Look at the first equation: Solve for x.

Add 3 to both sides:

x = 3 or x + 1 = 0 or x + 4 = 0

 

Look at the second equation: Solve for x.

Subtract 1 from both sides:

x = 3 or x = -1 or x + 4 = 0

 

Look at the third equation: Solve for x.

Subtract 4 from both sides:

x = 3      or      x = -1      or       x = -4

Guest Dec 30, 2017
 #2
avatar+90023 
+2

 x^3+2x^2-11x-12    =  0           we can write this as

 

x^3  + x^2  + x^2  - 11x  -  12 =  0     factor

 

x^2(x + 1)  +  ( x - 12) ( x + 1)  =  0

 

(x  + 1)  ( x^2  +  x  -   12)  = 0

 

(x + 1)  ( x + 4) ( x - 3)  =  0

 

Setting each factor to  0   and solving for x  gives the roots

 

x  = -4,  x  = -1    and  x  = 3

 

And their sum is    -2

 

 

cool cool cool

CPhill  Dec 30, 2017

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