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

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

View Question

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

View Question

The sides of a triangle are 5 cm, 12 cm, and 13 cm. What type of triangle is it?

View Question

A sum triples in 20 years at simple interest. What is the rate of interest per annum?

View Question

If x + 1/x = 5, what is the value of x^2 + 1/x^2?

View Question

What is the area of a sector of a circle with radius 14 cm and central angle 90°?

View Question

How many ways can 4 people sit in a row?

View Question

A man rows downstream at 6 km/h and upstream at 4 km/h. What is the speed of the stream?

View Question

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

View Question

If a = 2 and b = 3, what is the value of (a^2 + b^2)?

View Question