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liq [111]
2 years ago
10

Solve the equation X³+2X²-5X -6​

Mathematics
1 answer:
Natali [406]2 years ago
6 0

Answer: x = {-1, -3, 2}

<u>Step-by-step explanation:</u>

x³ + 2x² - 5x - 6 = 0

Use the rational root theorem to find the possible roots:  ±1, ±2, ±3, ±6

Use Long division, Synthetic division, or plug them into the equation to see which root(s) work <em>(result in a remainder of zero)</em>.

I will use Synthetic division.  Let's try x = 1

1 |  1    2    -5     -6

  |<u>  ↓    1      3     -2 </u>      

     1     3    -2    -8   ← remainder ≠ 0 so x = 1 is NOT a root

 Let's try x = -1

- 1 |  1     2    -5    -6

   |<u>  ↓    -1     -1     6 </u>      

      1     1     -6     0   ← remainder = 0 so x = -1 is a root!

The coefficients of the reduced polynomial are: 1, 1, -6  -->   x² + x - 6

Factor: x² + x - 6

          (x + 3)(x - 2)

Set those factors equal to zero to solve for x:

x + 3 = 0   --> x = -3

x - 2 = 0    --> x = 2

Using Synthetic Division and Factoring the reduced polynomial, we found

x = -1, -3, and 2

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