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 value of x if log(x) + log(4) = log(32)?

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

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

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If a:b = 7:9 and b:c = 5:6, what is a:c?

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If sin(A) = 1/2 and A is acute, what is the value of A?

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

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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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If a cone has a radius of 5 cm and a height of 12 cm, what is its slant height?

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If x = 3 and y = 4, what is the value of x^2 + y^2?

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