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

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A rectangle has a length of 10 cm and a width of 5 cm. What is the diagonal of the rectangle?

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What is the LCM of 15 and 20?

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If x + y = 10 and xy = 21, what is the value of x³ + y³?

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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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What is the sum of all even numbers between 1 and 50?

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The base of a triangle is 10 cm and its height is 6 cm. What is its area?

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What is the sum of the first 50 positive integers?

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

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The sum of the reciprocals of two numbers is 1/4. If one number is 12, what is the other?

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