Quadratic Equations PDF

PDF Name	Quadratic Equations
No. of Pages	9
PDF Size	0.30 MB
Language	English
PDF Category	Education & Jobs
Source / Credits	mathcentre.ac.uk
Uploaded By	Pradeep

Quadratic Equations - Summary

A quadratic equation in the variable x is a mathematical expression that takes the form ax² + bx + c = 0, where a, b, and c are real numbers, and a isn’t equal to zero. Quadratic equations are the polynomial equations of degree 2 in one variable, making them essential in math. This means they can be written as f(x) = ax² + bx + c = 0, with a, b, c ∈ R and a ≠ 0. This is the general representation of a quadratic equation where ‘a’ is the leading coefficient, and ‘c’ is known as the absolute term of f(x). The solutions for x that satisfy this quadratic equation are referred to as the roots of the quadratic equation (α, β).

Understanding Quadratic Equations

A quadratic polynomial becomes a quadratic equation when it is set to zero. The values of x that satisfy this equation are its roots.

Quadratic Equation Formula

The solutions, or roots, of a quadratic equation can be found using the quadratic formula:

(α, β) = [-b ± √(b² – 4ac)]/2a

Roots of Quadratic Equations

The values of the variables that satisfy the quadratic equation are called its roots. Specifically, x = α is a root of the quadratic equation f(x) if f(α) = 0.

The real roots of the equation f(x) = 0 are where the curve y = f(x) intersects the x-axis.