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 remainder when 5^100 is divided by 3?

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What is the cube root of 729?

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A number is increased by 20% and then decreased by 10%. What is the net change?

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What is the HCF of 48 and 180?

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

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If x^2 - 5x + 6 = 0, what are the roots?

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If x^2 - 6x + 9 = 0, what is the value of x?

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

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If a:b = 3:4 and b:c = 5:6, what is a:c?

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

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