Quadratic Formula or Quadratic Equation
More Lessons for Grade 6
Math Worksheets
Factoring Out Common Factors (GCF).
Factoring Quadratic Equations using Perfect Square Trinomial (Square of a Sum or Square of a Difference) or Difference of Two Squares.
Factoring Quadratic Equations where the coefficient of x2 is 1.
Factoring Quadratic Equations by Completing the Square
Factoring Quadratic Equations where the coefficient of x2 is greater than 1
In this lesson, we will learn how to use the Quadratic Formula to solve quadratic equations. This method is usually used when it is too difficult to solve the quadratic equation by factoring and other methods or when the solutions are not integers.
What is the Quadratic Formula?
The following diagrams gives the Quadratic Formula and how to use it to solve quadratic equations. Scroll down the page for more examples and solutions of the quadratic formula.
Given the quadratic equation ax2 + bx + c, we can find the values of x by using the Quadratic Formula:
Let us consider an example.
Example: Find the values of x for the equation: 4x2 + 26x + 12 = 0
Step 1: From the equation:
a = 4, b = 26 and c = 12
Step 2: Plug into the formula. The ± sign means there are two values, one with + and the other with –.
Answer: :
Quadratic equations have at most two real solutions, as in the example above.
However, some quadratic equations have only one real solution. If the quadratic equation has only one solution, the expression under the square root symbol in the quadratic formula is equal to 0, and so adding or subtracting 0 yields the same result.
Other quadratic equations have no real solutions; for example, In this case, the expression under the square root symbol is negative, so the entire expression is not a real number.
Have a look at the following videos for more examples on the use of quadratic formula to solve equations:
Using the Quadratic Formula to find solutions to quadratic equations
Example:
Solve 9x2 - 9x + 2 = 0
Solve 3x2 + √11x + 2 = 0 Example:
Solve 3x2 + 5x = 7 Solving quadratic equations using the quadratic formula.
Examples:
Solve x2 - 5x - 6 = 0
Solve 2x2 - 4x - 7 = 0
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