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Viefleur [7K]
3 years ago
8

What is the solutions to the equation?

Mathematics
1 answer:
victus00 [196]3 years ago
4 0
Hi,

Solving:

x^{3} + 3x^{2} - 4x - 12 = 0 \\ {x}^{2} \times (x + 3) - 4x - 12 = 0 \\ {x}^{2} \times (x + 3) - 4(x - 3) = 0 \\ (x + 3) \times ( {x}^{2} - 4) = 0 \\ x + 3 = 0 \\ {x}^{2} - 4 = 0 \\ \\ (results) \\ x1 = - 3 \\ x2 = - 2 \\ x3 = 2

Hope this helps.
r3t40
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Type the correct answer in each box. (____)
trapecia [35]

Answer:

1. -16; 2. +64; 3. 16

Step-by-step explanation:

The formula for the volume of a cylinder is

V = πr²x

Data:

r = (x - 8)   mm

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Calculations:

1. Find the cubic equation  

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Divide each side by π

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1024 =    x³ - 16x² + 64x

x³ - 16x² + 64x - 1024 = 0

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The general formula for a third-degree polynomial is

f(x) = ax³ + bx² + cx + d

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a = 1; d = -1024

According to the <em>rational roots theorem</em>, the possible roots are

factors of d/factors of a

Factors of d = ±1, ±2, ±4, ±8, ±16, ± 32, ± 64, ±128, ±256, ±512, ±1024

Factors of a = ±1

Potential roots are x = ±1, ±2, ±4, ±8, ±16, ± 32, ± 64, ±128, ±256, ±512, ±1024

That's a lot of possibilities to check by trial and error. I will just use the one that works.

Try x = 16 by synthetic division.

16|1  -16   64  -1024

  <u>|     16     0   1024 </u>

   1     0   64        0

So,

(x³ - 16x² + 64x - 1024)/(x – 16) = x² + 64

and

(x - 16)(x² + 64) = 0

x - 16 = 0        x² + 64 =    0

     x = 16       x²         = -64

                       x          =  ±8i

There is only one real root: x = 16 mm

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Step-by-step explanation:

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