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What is the Quadratic Formula?

Updated on December 6, 2012

The Basic of the Quadratic

The quadratic formula is an essential part of algebra and understanding how to solve problem with a specif form.

ax2 + bx + c = 0 - this form of equation can be solved using the quadratic equation

Every quadratic equation has two solutions known as roots. Quadratic equations can also be solved using graphing techniques or factoring. The method shown here is using the quadratic equation in order to find the roots.

The Quadratic Equation

What is the point?

The goal is to find x. X is the unknown variable in the polynomial equation.

Why can't "a" be 0?

Remember a can not equal 0 - otherwise this equation won't work. If a = 0 than it isn't the correct format because a times any variable will always be 0 so the equation would not have a power of 2. and would only be bx +c

The Quadratic Equation

Quadratic Equation
Quadratic Equation | Source

EXAMPLES of the Quadratic Equation

The first thing we need are defined variable for a, b, & c.

For this example a=2, b=4, & c=-6

I am using this numbers because they will work out to a nice even number

You are looking for two roots of the quadratic. Remember the sign that says plus or minus that is because you will need to do the last part of the equation twice - once in addition and once in subtraction.

numbers plugged into variables
numbers plugged into variables | Source
simplify | Source

Solving for the Frist root with addtion


Solving the first root

In order to solve the first root we are going to use addition in the equation

Solving the Second Root


Solving the second root

In order to find the second root we will go back to where we left off before we solving the first root and use subtraction instead of addition.


How to Check Your Roots

In order to check your anser you must check your roots. If it is correct the sum of the roots should be equal to -b/a


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    • Missy Mac profile image

      Missy Mac 4 years ago from Illinois

      Thank you! This is a great hub. I look for more of your math hubs.

    • kthix10 profile image

      kthix10 5 years ago from IL

      I agree this one was just the basics. I plan to write more in the future so stay tuned

    • rahul0324 profile image

      Jessee R 5 years ago from Gurgaon, India

      Nice hub! I would love to add more detail though... like the variation of roots according to the value of the discriminant and the geometrical representation of ellipse parabola and hyperbola according different values in a second degree polynomial... but... Reading as a student finding the basics... the hub is great :)

    • profile image

      Headfullofsound 5 years ago

      As an up-and-coming Math major, this is a real help! Will you marry me (to my boyfriend someday)?