A quadratic equation is an equation with a variable to the second power as its highest power term. For example, in the quadratic equation 3x^{2}  5x2=0:
When can I solve by taking square roots?
Quadratic equations without xterms such as 2x^{2} = 32 can be solved without setting a quadratic expression equal to 0. Instead, we can isolate x^{2} and use the square root operation to solve for x.
When solving quadratic equations by taking square roots, both the positive and negative square roots are solutions to the equation. This is because when we square a solution, the result is always positive.
For example, for the equation x^{2} = 4, both 2 and 2 are solutions:
When solving quadratic equations without xterms:
Example: What values of x satisfy the equation 2x^{2} = 18?
Sol:
The following values of x satisfy the equation 2x^{2} = 18:
The zero product property states that if ab = 0, then either a or b is equal to 0.
The zero product property lets us solve factored quadratic equations by solving two linear equations. For a quadratic equation such as (x5)(x + 2) = 0, we know that either x 5 = 0 or x + 2 = 0. Solving these two linear equations gives us the two solutions to the quadratic equation.
To solve a factored quadratic equation using the zero product property:
If we can write a quadratic expression as the product of two linear expressions (factors), then we can use those linear expressions to calculate the solutions to the quadratic equation.
We'll focus on factorable quadratic equations with 1 as the coefficient of the x^{2} term, such as x^{2 }2x  3 = 0. For more advanced factoring techniques, including special factoring and factoring quadratic expressions with x^{2} coefficients other than 1, check out the Factoring quadratic and polynomial expressions.
Recognizing factors of quadratic expressions takes practice. The factors will be in the form (x + a) (x + b), where a and b fulfill the following criteria:
For example, we can solve the equation x^{2}  2x  30 by factoring x^{2}  2x  3 into (x + a) (x + b), where:
3 and 1 would work:
This means we can rewrite x^{2}  2x  3 = 0as (x  3)(x + 1) = 0 and solve the quadratic equation using the zero product property. Keep mind that a and b are not themselves solutions to the quadratic equation!
When solving factorable quadratic equations in the form x^{2} + bx + c = 0:
Not all quadratic expressions are factorable, and not all factorable quadratic expressions are easy to factor. The quadratic formula gives us a way to solve any quadratic equation as long as we can plug the correct values into the formula and evaluate.
What are the steps?
To solve a quadratic equation using the quadratic formula:
75 videos238 docs91 tests

1. What are quadratic equations and why are they important in mathematics? 
2. How can square roots be used to solve quadratic equations? 
3. What is the Zero Product Property and how is it used to solve quadratic equations? 
4. How do you solve factorable quadratic equations? 
5. What is the Quadratic formula and how is it used to solve quadratic equations? 

Explore Courses for Commerce exam
