Topic Details (Notes format)

How to Solve Quadratic Equations by Factoring

Subject: Mathematics

Book: Maths Mastery

Factoring is a more intuitive method for solving ax² + bx + c = 0 when the polynomial can be expressed as a product of two binomials. For instance, x² + 5x + 6 factors to (x + 2)(x + 3) = 0, giving solutions x = –2 or x = –3. The approach requires identifying two numbers that multiply to ac and add to b. While factoring is not always possible with neat integers, it’s efficient when applicable. This method is widely used in geometry, business break-even analyses, and logic puzzles. Practicing with different coefficients develops a keen sense for pattern recognition and polynomials.

Practice Questions

A sum of money doubles itself in 5 years at simple interest. What is the rate of interest?

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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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A man invests Rs. 5000 at 5% per annum simple interest. What is the total amount after 3 years?

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If the sum of three consecutive integers is 96, what are the integers?

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How many ways can 4 people sit in a row?

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

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What is the sum of the first 50 positive integers?

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What is the HCF of 72 and 120?

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If a:b = 2:3 and b:c = 4:5, what is a:c?

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If sin(θ) = 3/5 and θ is an acute angle, what is tan(θ)?

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