Create and solve one-variable equations and inequalities, including absolute-value, linear, quadratic, simple rational, and exponential cases.
Create and solve a quadratic inequality from context
Problem
A business models profit by \(P(x)=x^{2}-5x+6\), where \(x\) is a nonnegative real production index. Use the displayed \(\text{zero}~\text{target}\) to write and solve the quadratic inequality for positive profit, then report every allowable solution in the contextual domain.
The profit model, zero target, and nonnegative domain are shown on scaled axes without labeled roots or solution intervals.Open full size
Big Picture
What this problem is really about
Positive profit asks where the quadratic lies strictly above the zero target, not merely where it touches that line. We’ll factor to find the boundary values, determine the sign on the intervals they create, exclude boundaries because the inequality is strict, and finally intersect the algebraic solution with the nonnegative production domain.
Inside Gozunta
Turn the preview into practice.
More than a preview
Gozunta lets you study this problem—and more than 10,000 others.
Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.
