Subject: Mathematics
Book: Maths Mastery
Polynomial inequalities like x²–5x+4≥0 require factoring to find critical points: (x–4)(x–1)≥0. Then test intervals around the roots x=1, x=4 to see where the product is nonnegative. Typically, you place the roots on a number line, check sign in intervals (–∞,1), (1,4), (4,∞), and choose intervals that satisfy ≥0. This approach extends to cubic or higher polynomials. In engineering or advanced math, polynomial inequalities define stability ranges or design constraints. Mastery ensures precise solutions to complex numeric intervals in real-life contexts.
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