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

If a right triangle has legs of 9 cm and 12 cm, what is the length of the hypotenuse?

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What is the cube root of 729?

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If a cone has a base radius of 3 cm and height of 4 cm, what is its slant height?

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

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If log(100) = 2 and log(10) = 1, what is log(1000)?

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

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The sides of a triangle are 13 cm, 14 cm, and 15 cm. What is its area?

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If 2x = 16, what is the value of x?

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

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