Quadratic Inequalities — Quiz

Question 2 • Advanced Algebra: Concepts and Connections

What is the solution set to the inequality 5 open paren x minus 2 close paren open paren x plus 4 close paren is greater than 0 ?

Answer

start set x such that x is greater than negative 4 and x comma negative 4 and x is less than 2 end set

start set x such that x is less than negative 2 or x comma negative 2 or x is greater than 4 end set

start set x such that x is less than negative 4 or x comma negative 4 or x is greater than 2 end set

start set x such that x is greater than negative 2 or x comma negative 2 or x is less than 4 end set

Explanation

The constant 5 is positive, so it does not change where the product is positive. The factors are zero at x = −4 and x = 2; testing the intervals shows (x − 2)(x + 4) is positive outside those values. Thus the solution is x < −4 or x > 2, which is choice A.

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