MCR 3U1
Unit 3
Lesson 5: Solving Quadratic Equations
A quadratic equation can be written in the form ax 2  bx  c  0 , where a  0 .
The terms of a quadratic equation are named as follows:
ax2 + bx + c = 0
Quadratic
term
Linear
term
Constant
term
Solving Quadratics
There are many methods for solving quadratic equations. By solving the equation, we are
determining the roots (zeroes/x-intercepts/solutions) of the quadratic function.
1. Reducing an equation with no linear terms to the form x 2  c .
Example 1: x 2  5  0
2. Graphing – the roots of the equation are where the graph crosses the x-axis.
Example 2:
y




x











3. Factoring, using any of the given methods.
Example 3: x 2  7 x  10  0


MCR 3U1
Unit 3
4. Completing the square.
Example 4: Complete the square to determine the maximum value:  5 x 2  30 x  10  0 .
5. Using the quadratic formula.
Example 5: Solve 2 x 2  3 x  2 using the quadratic formula.
Note: You should only use the quadratic formula when you cannot factor the equation. Also,
you may want to leave your final answer as an exact value, depending on the situation.
Example 6: Represent and solve a problem using a quadratic equation. You are given that a
rectangle has an area of 330 m2. One side is 7 m longer than the other. What are the dimensions
of the rectangle?