Problem

Can we find a quadratic inequality for each region of the Venn diagram?

The regions are defined as follows.

A: The solution set is a subset of \(x≤1\).

B: The solutions are given by \(a≤x≤b\) where \(a\) and \(b\) are real numbers.

C: The inequality is satisfied by \(x=4\), e.g. \(x=4\) satisfies the inequality \(x≥2\).

Diagram shows three intersecting circles A, B and C

Here are some possible inequalities. Start by placing these into the correct region of the Venn diagram.

\(x^2≤9\)

\(11x≥2x^2\)

\(x^2+3≥2\)

\(3x^2≥21x-30\)

\(x^2≤-x\)

\(x^2≤x-2\)

\(6x^2-1≥5x\)

\(-2x^2≤x-6\)