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

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If sin(A) = 3/5 and cos(B) = 5/13, where A and B are acute angles, what is sin(A+B)?

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If the radius of a circle is doubled, what happens to its area?

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What is the area of an equilateral triangle with side length 10 cm?

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The angles of a quadrilateral are in the ratio 3:4:5:6. What is the largest angle?

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A car travels 240 km in 4 hours. What is its average speed?

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A train 120 meters long is moving at a speed of 54 km/h. How long will it take to pass a pole?

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