Welcome to the quadratic equation section. It gives you not only the
answers, but also the complete solution for your equation, so that you
can understand better how to solve quadratic equations.
Quadratic Equations Explained
A quadratic equation is an equation that looks like this:
where a, b, and c are numbers, called coefficients.
ax2+bx+c = 0,
x2+3x+4 = 0
You can think about a quadratic equation in terms of a graph of a quadratic function, which is called a parabola. The equation means that you have to find the points
on the horizontal axis (x) where the graph intersects with the axis.
To solve a quadratic equation, you have to calculate a number
called discriminant, usually denoted as d:
d = b2-4ac
Depending on the value of d, there are the folowing three possibilities:
*Note: For those of you who are inclined to verify this formula,
here's how to arrive to it: try to convert a standard quadratic equation
- Discriminant d is greater than zero.
The equation has two solutions.
x1,2 = -b ± sqrt( b2-4ac )
- Discriminant is zero. There is only one solution.
x = -b/2a
- Discriminant is less than zero. No solutions are defined.
Note: for those of you who study complex numbers, there is
a complex solution. If you do not know what complex numbers are,
skip this part.