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Lesson: Quadratic Inequalities

Sample Question Videos

Worksheet • 11 Questions • 2 Videos

Q1:

Solve the inequality βˆ’ 2 π‘₯ + π‘₯ β‰₯ βˆ’ 6 2 .

  • A  βˆ’ 3 2 , 2 
  • B  βˆ’ 3 2 , 2 
  • C ℝ βˆ’  βˆ’ 3 2 , 2 
  • D ℝ βˆ’  βˆ’ 3 2 , 2 

Q2:

Solve the inequality 6 π‘₯ βˆ’ 5 π‘₯ β‰₯ 4 2 .

  • A ℝ βˆ’  βˆ’ 1 2 , 4 3 
  • B ℝ βˆ’  βˆ’ 1 2 , 4 3 
  • C  βˆ’ 1 2 , 4 3 
  • D  βˆ’ 1 2 , 4 3 

Q3:

Solve the inequality 4 π‘₯ + 8 π‘₯ β‰₯ 5 2 .

  • A ℝ βˆ’  βˆ’ 5 2 , 1 2 
  • B ℝ βˆ’  βˆ’ 5 2 , 1 2 
  • C  βˆ’ 5 2 , 1 2 
  • D  βˆ’ 5 2 , 1 2 

Q4:

Which of the following describes the solution set of the inequality π‘₯ βˆ’ 7 π‘₯ + 1 2 > 0 2 ?

  • A ℝ βˆ’ [ 3 , 4 ]
  • B [ 3 , 4 ]
  • C ℝ βˆ’ ] 3 , 4 [
  • D ℝ βˆ’ ] βˆ’ 4 , βˆ’ 3 [
  • E ℝ βˆ’ [ βˆ’ 4 , βˆ’ 3 ]

Q5:

Write the interval describing all solutions to the inequality 3 0 + 1 3 π‘₯ βˆ’ π‘₯ > 0 2 .

  • A ] βˆ’ 2 , 1 5 [
  • B [ βˆ’ 2 , 1 5 ]
  • C ℝ βˆ’ [ βˆ’ 1 5 , 2 ]
  • D ℝ βˆ’ ] βˆ’ 1 5 , 2 [
  • E ] βˆ’ 1 5 , 2 [

Q6:

Find all solutions to the inequality ( π‘₯ + 4 ) + ( π‘₯ + 1 ) ( π‘₯ βˆ’ 1 6 ) < 0 2 . Write your answer as an interval.

  • A  0 , 7 2 
  • B ℝ βˆ’  βˆ’ 7 2 , 0 
  • C  βˆ’ 7 2 , 0 
  • D ℝ βˆ’  βˆ’ 7 2 , 0 

Q7:

A mobile phone company has the following cost and revenue functions: 𝐢 ( π‘₯ ) = 8 π‘₯ βˆ’ 6 0 0 π‘₯ + 2 1 5 0 0 2 and 𝑅 ( π‘₯ ) = βˆ’ 3 π‘₯ + 4 8 0 π‘₯ 2 . State the range for the number of mobile phones they can produce while making a profit. Round your answers to the nearest integer that guarantees a profit.

  • A28–70 mobile phones
  • B27–70 mobile phones
  • Cmore than 160 mobile phones
  • D28–71 mobile phones

Q8:

Find the interval describing all solutions to the inequality π‘₯ ≀ 4 2 .

  • A [ βˆ’ 2 , 2 ]
  • B ℝ βˆ’ [ βˆ’ 2 , 2 ]
  • C ℝ βˆ’ ] βˆ’ 2 , 2 [
  • D ] βˆ’ 2 , 2 [

Q9:

Given 𝑓 = 3 π‘₯ βˆ’ 9 π‘₯ + 6 2 , find the solution set of the inequality 𝑓 ( π‘₯ ) < 0 by determining the sign of 𝑓 .

  • A 𝑓 ( π‘₯ ) is negative when π‘₯ ∈ ] 1 , 2 [ , which is the solution set of the inequality.
  • B 𝑓 ( π‘₯ ) is negative when π‘₯ ∈ ℝ βˆ’ [ 1 , 2 ] , which is the solution set of the inequality.
  • C 𝑓 ( π‘₯ ) is negative when π‘₯ ∈ ℝ βˆ’ ] 1 , 2 [ , which is the solution set of the inequality.
  • D 𝑓 ( π‘₯ ) is negative when π‘₯ ∈ [ 1 , 2 ] , which is the solution set of the inequality.

Q10:

Write the interval describing all solutions to the inequality βˆ’ π‘₯ βˆ’ 2 π‘₯ + 1 6 8 β‰₯ 0 2 .

  • A [ βˆ’ 1 4 , 1 2 ]
  • B [ βˆ’ 1 2 , 1 4 ]
  • C ℝ βˆ’ [ βˆ’ 1 4 , 1 2 ]
  • D ℝ βˆ’ ] βˆ’ 1 4 , 1 2 [
  • E ] βˆ’ 1 4 , 1 2 [

Q11:

Solve the inequality ( π‘₯ βˆ’ 5 ) ( π‘₯ βˆ’ 7 ) β‰₯ βˆ’ 5 π‘₯ + 3 5 .

  • A π‘₯ ∈ ℝ βˆ’ ] 0 , 7 [
  • B π‘₯ ∈ [ 0 , 7 ]
  • C π‘₯ ∈ ℝ βˆ’ { 0 , 7 }
  • D π‘₯ ∈ ℝ βˆ’ [ 0 , 7 ]
  • E π‘₯ ∈ ] 0 , 7 [
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