A free quadratic equation calculator that shows and explains each step in solving your quadratic equation.
A quadratic equation is an function that has the form: ax2
+ bx + c = 0. In this equation, a, b, and c are constants. X is unknown. The constants a and b, are referred to as coefficients. Further, a cannot equal to 0 in the equation ax2
+bx+c=0. If a is 0, then ax2
=0, and the equation becomes 0+bx+c=0, or bx+c=0. The equation bx+c=0 is a linear equation, and not a quadratic equation.
Solving a linear equation is pretty straightforward. Solving a quadratic equation requires more work. Fortunately, you have this handy-dandy quadratic equation calculator. All kidding aside, quadratic equations can be quickly solved using the quadratic formula
, which is the same technique used by this quadratic equation calculator. Try it, and it will explain each of the steps to you. The quadratic formula is written:
Solving a quadratic equation will always result in 2 solutions for x. These solutions are called roots. These roots may both be real numbers or, they may both be complex numbers. Rarely, both roots may have the same value, producing one solution for x.
You may be asking yourself, "Why is this stuff so important?" Quadratic equations are needed to find answers to many real-world problems. The geometry of a parablolic dish antenna is one example of an application of quadratic equations.
As mentioned above, in the equation ax2
+bx+c=0, a cannot be zero. If a were 0, then ax2
= 0 for any value of x, so our equation becomes 0 + bx + c = 0, which is the same as bx + c = 0, which is no longer a quadratic equation. In fact, bx + c = 0 is a linear equation, which is much simpler to solve than a quadratic equation.
We hope you find this quadratic equation calculator useful. We encourage you to try it with different values, and to read the explanation for how to reach your answer. But, if you just want to use it to calculate the answers to your quadratic equations, that's cool too. Thank you for using Quadratic-Equation-Calculator.com.
for a random example of a quadratic equation.