quadratic compound inequality

Practise quadratic compound inequality with an original VectorPaths question, worked explanation and related VCE Methods practice.

1 practice marks

Original practice question

Given $f(x) = x^2 - 6x + 5$, find the values of $x$ for which $-4 < f(x) < 0$.

Worked explanation

• Solve the upper inequality

  \(x^2-6x+5<0\) factors as \((x-1)(x-5)<0\), giving \(1<x<5\).

• Enforce the lower inequality

  \(x^2-6x+5>-4\) is \((x-3)^2>0\), which excludes \(x=3\). Combining both strict inequalities gives \((1,3)\cup(3,5)\).

\((1,3)\cup(3,5)\)

Original VectorPaths practice; not an official VCAA question or marking rubric.