Topic Details (Notes format)

How to Solve Polynomial Inequalities

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.

Practice Questions

What is the value of log₃(27)?

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A cube has a side length of 4 cm. What is its volume?

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If x:y = 2:3 and z:y = 4:3, what is x:z?

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If the average of five consecutive odd numbers is 25, what is the largest number?

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If a = 2 and b = 3, what is the value of (a^2 + b^2)?

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If x^3 - 3x^2 + 4 = 0, what is one root of the equation?

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If a = 5 and b = 12, what is the length of the hypotenuse of a right triangle?

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What is the sum of all odd numbers from 1 to 99?

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What is the greatest common divisor (GCD) of 36 and 48?

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If sin(θ) = 0.6 and θ is acute, what is cos(θ)?

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