Solving Quadratic Equations - Worksheet MCR3U

Discriminant

Determines number of roots in quadratics.

Quadratic Formula

Formula to find roots: x = (-b±√D)/(2a).

Roots

Solutions to the quadratic equation.

Exact Answers

Solutions expressed without decimal approximation.

Right Triangle

Triangle with one 90-degree angle.

Pipe Lengths

Lengths used to form a right triangle.

One Root

Quadratic has a single solution.

No Roots

Quadratic has no real solutions.

Two Roots

Quadratic has two distinct solutions.

Quadratic Equation

Polynomial equation of degree two.

Solving Quadratics

Finding values of x that satisfy the equation.

Method of Solving

Approaches include factoring, completing square, or formula.

Example of Quadratic

x² - 10x + 25 = 0.

Pipe Cutting Problem

Finding length to cut for triangle formation.

Quadratic Coefficients

Values of a, b, and c in ax² + bx + c.

Negative Discriminant

Indicates no real roots exist.

Quadratic Roots Calculation

Process of determining x values from equations.