Topic Details (Notes format)

How to Solve Quadratic Equations (Using the Quadratic Formula)

Subject: Mathematics

Book: Maths Mastery

Quadratic equations typically appear in the form ax² + bx + c = 0, where a, b, and c are constants. The quadratic formula, x = (–b ± √(b² – 4ac)) / (2a), is a universal method to find the roots (solutions). For example, to solve x² + 5x + 6 = 0, identify a=1, b=5, c=6. Plug these into the formula: x = (–5 ± √(25 – 24)) / (2) = (–5 ± 1) / 2, so the solutions are x = –3 and x = –2. Quadratic equations describe projectile motion, optimization problems, and many natural phenomena. Mastering the formula ensures you can handle everything from physics tasks to architecture and beyond.

Practice Questions

A number is increased by 20% and then decreased by 10%. What is the net change?

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The LCM of 12 and 15 is:

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

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A sum of money triples itself in 12 years at simple interest. What is the rate of interest per annum?

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

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If a:b = 5:7 and b:c = 6:11, what is a:c?

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If x^2 - 5x + 6 = 0, what are the roots?

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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 LCM of two numbers is 60, and their HCF is 5. If one of the numbers is 20, what is the other number?

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What is the sum of the first 10 positive even numbers?

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