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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 4: Q. 8 (page 247)

Solve the equation : $x^{3} - 6 x^{2} + 8 x = 0$

Short Answer

Expert verified

The solution of the equation is $x = 0, 2, 4$

Step by step solution

Given information

We are given an equation $x^{3} - 4 x^{2} + 8 x = 0$

We separate the terms

We have,

$x^{3} - 6 x^{2} + 8 x = 0 x (x^{2} - 6 x + 8) = 0 x = 0 o r x^{2} - 6 x + 8 = 0$

Now solve the quadratic equation

We get,

$x^{2} - 6 x + 8 = 0 x^{2} - 4 x - 2 x + 8 = 0 x (x - 4) - 2 (x - 4) = 0 (x - 4) (x - 2) = 0 x = 4 o r x = 2$

Conclusion

The roots of the given equation are $x = 0, 2, 4$

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Solve the equation :x3-6x2+8x=0

Short Answer

Step by step solution

Given information

We separate the terms

Now solve the quadratic equation

Conclusion

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Solve the equation : $x^{3} - 6 x^{2} + 8 x = 0$