Cubic inequalities and endpoint inclusion: check 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle P(x)=\)\(\left(x - 22\right) \left(x - 17\right) \left(x - 16\right)\). Use a sign chart to analyse P.
Find the left endpoint of the bounded interval where \(\displaystyle P\ge 0\).
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Cubic inequalities and endpoint inclusion: review variant 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle P(x)=\)\(\left(x - 21\right) \left(x - 19\right) \left(x - 17\right)\). Use a sign chart to analyse P.
Find the left endpoint of the bounded interval where \(\displaystyle P\ge 0\).
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Cubic inequalities and endpoint inclusion: check 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle P(x)=\)\(\left(x - 21\right) \left(x - 19\right) \left(x - 17\right)\). Use a sign chart to analyse P.
Find the right endpoint of the bounded interval where \(\displaystyle P(x)\ge 0\).
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Cubic inequalities and endpoint inclusion: review variant 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle P(x)=\)\(\left(x - 24\right) \left(x - 21\right) \left(x - 18\right)\). Use a sign chart to analyse P.
Find the right endpoint of the bounded interval where \(\displaystyle P(x)\ge 0\).
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Cubic inequalities and endpoint inclusion: check 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle P(x)=\)\(\left(x - 24\right) \left(x - 21\right) \left(x - 18\right)\). Use a sign chart to analyse P.
Find the largest root.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Cubic inequalities and endpoint inclusion: review variant 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle P(x)=\)\(\left(x - 27\right) \left(x - 22\right) \left(x - 20\right)\). Use a sign chart to analyse P.
Find the largest root.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Cubic inequalities and endpoint inclusion: check 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle P(x)=\)\(\left(x - 24\right) \left(x - 20\right) \left(x - 19\right)\). Use a sign chart to analyse P.
Evaluate P at the midpoint of the last two roots.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Cubic inequalities and endpoint inclusion: review variant 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle P(x)=\)\(\left(x - 27\right) \left(x - 22\right) \left(x - 20\right)\). Use a sign chart to analyse P.
Evaluate P at the midpoint of the last two roots.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.