4
QuizMultiple Choice

Quadratic Inequalities — Quiz

Question 4 • Advanced Algebra: Concepts and Connections

What are the solutions to the inequality open paren x minus 3 close paren times open paren x plus 5 close paren is less than or equal to 0 ?

Answer
A
start set x such that 3 is less than or equal to x comma x is less than or equal to 5 end set
B
start set x such that negative 5 is less than or equal to x comma x is less than or equal to negative 3 end set
C
start set x such that negative 3 is less than or equal to x comma x is less than or equal to 5 end set
D
start set x such that negative 5 is less than or equal to x comma x is less than or equal to 3 end set

Explanation

The factors are zero at x = 3 and x = -5. The product (x - 3)(x + 5) is less than or equal to zero between these roots, including the endpoints where the product equals zero. Thus the solution is -5 ≤ x ≤ 3, choice B.

AI-written and checked against the verified answer.

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