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

The simple interest on Rs. 4000 at 5% per annum for 2 years is:

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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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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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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 2x = 16, what is the value of x?

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If the average of five consecutive odd numbers is 25, what is the largest number?

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If x - y = 5 and x + y = 15, what is the value of x?

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A train 150 m long passes a pole in 15 seconds. What is its speed?

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What is the sum of all angles in a hexagon?

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If x^2 + 4x + 4 = 0, what is the value of x?

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