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

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If a + b = 10 and ab = 21, what is the value of a^2 + b^2?

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If the radius of a circle is 7 cm, what is its circumference?

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What is the value of log₃(27)?

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If 5x - 2 = 13, what is the value of x?

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If the sum of three consecutive integers is 72, what are the integers?

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The perimeter of a rectangle is 50 cm, and its length is 15 cm. What is its width?

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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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If two complementary angles differ by 30°, what are the angles?

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What is the length of the diagonal of a square with a side length of 7 cm?

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