PRECALCULUS:GRAPHICAL,...-W/ACCESS
PRECALCULUS:GRAPHICAL,...-W/ACCESS
10th Edition
ISBN: 9780134781945
Author: Demana
Publisher: PEARSON
Expert Solution & Answer
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Chapter P.7, Problem 27E
Solution

Solve the cubic inequality graphically.

  −2⋅077≤x≤0⋅167   or x≥1⋅911

Given:

The inequality is, 3x3−12x+2≥0

Concept Used:

  • The relationship between two values that are not equal is defined by inequalities.
  • Inequality means not equal.
  • Generally, if two values are not equal, we use “not equal symbol (?)”. But to compare the values, whether it is less than or greater than, different inequalities are used.
  • Factorization is the process of reducing the bracket of a quadratic equation, instead of expanding the bracket and converting the equation to a product of factors which cannot be reduced further. 

Calculation:

  3x3−12x+2≥0

The graph of 3x3−12x+2≥0 is −

  PRECALCULUS:GRAPHICAL,...-W/ACCESS, Chapter P.7, Problem 27E

  −2⋅077≤x≤0⋅167   or x≥1⋅911

Note that the given inequality is true for the values of −2⋅077≤x≤0⋅167 and for the values of x≥1⋅911

Thus, the solution of the given inequality is −2⋅077≤x≤0⋅167   or x≥1⋅911

Interval notation [−2⋅077,0⋅167 ]∪[1⋅911,∞)

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Chapter P.7, Problem 26E
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Chapter P.7, Problem 28E

Chapter P Solutions

PRECALCULUS:GRAPHICAL,...-W/ACCESS

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