If so, then here it is the one-stop solution for solving discriminant, real and complex roots with formula. It's very easy to use and 100% free. Also, in this article, we will discuss the formula, symbols, and how we can determine the discriminant and roots.
The Quadratic name comes from "Quad". Also, we can call it "Square" (Like x2). It is a solution of a second-order polynomial equation with three coefficients.
We can write the equation in standard form like this:
Here, A, B, and C are the coefficients or we can call it "Known Numbers".
Whereas, the 'x' is the unknown variable that we need to find out using the Quadratic Formula.
The following are some examples for better understanding.
|3x2 + 4x + 1 = 0||Here a=3, b=4, and c=1|
|2x2 - 4x = 0||You can see there is just 2 coefficients values at left side. So, we can figure our the values like this:
|4x + 2 = 0||It is not a quadratic equation. Because there is no x2 value. So, 'a' is counted as 0.|
Sometimes the quadratic equations are not in standard form. So, we have to move or expand some coefficients to convert it into standard form.
Let's see some examples:
|Disguise Form||Rearrangements||Standard Form||Coefficients|
|2x2 = 5x - 4||Move right values to left side||2x2 - 5x + 4 = 0||a=2, b=-5, c=4|
|4(y2 + 3y) = 2||Expand left side and move 2 to left||4y2 + 12y - 2 = 0||a=4, b=12, c=-2|
The formula looks like below and we can use it to find the "x" value.
Our quadratic equation solver determines the Discriminant values, whether it is greater than, less than, or equal to 0.
If b2 - 4ac is,
There are various ways to calculate the discriminant and roots which are given below.
In this article, we will only discuss the third method. Which is using the quadratic formula. Also, it is the most straightforward way to find the roots. Even more, the quadratic equation calculator uses the same concept behind the hood.
Let's take some examples to understand the process step by step.
First of all, we have to arrange the equation in standard form like this: ax2 + bx + c = 0.
Take -3 from right to left-hand side. As a result, we get:
Now look at the formula and figure out what things are known and unknown. Also, put them in their position.
In the formula, you have to put a, b, and c in their respective places.
In our case, the values are:
After putting them in the formula, we get,
x = -5 ± √(52) - 4(2 x 3)
2 x 2
= -5 ± √25 - 24
= -5 ± 1
As you can see, the discriminant(b2 - 4ac) = 1 that is > 0. So, there are two real roots.
For the First Root:
x = -5 + 1
x = -1
For the Second Root:
x = -5 - 1
x = -1.5
Hence, the roots of 2x2 + 5x + 3 = 0 are -1 and -1.5.
Here Coefficients are: a = 4, b = 15, c = 20.
So, first of all, let's find the discriminant:
Δ = b2 − 4ac
= 152 - 4(4 x 20)
= 152 - 4(80)
= 225 - 320
Note that, the discriminant is -95. That is negative. So, we will get 2 complex roots.
Now let's find the roots.
x = -15 ± √(-95)
2 x 4
x = -15 ± √(-95)
√(-95) = 1.21835i
(i = √−1, Imaginary number)
So, x = -15 ± 1.21835i
Final Answer: -1.875 ± 1.21835i
A linear equation has only one solution or root. In the standard form of quadratic equation, if 'a' becomes 0, then the equation evaluates to bx + c = 0. Hence, it becomes a linear equation. The solution of a linear equation is given by:
The graph of a quadratic equation is basically a U-shaped curve called Parabola. The shape of the curve depends upon the sign of 'A' (the coefficient with x2).
The process is very simple. But you need a smart device like a computer, smartphone, or iPad with a browser installed. Also, your device must be connected with the Internet. Because this is an online calculator. So, the internet is compulsory.
After that, open the Quadratic Formula Calculator on your device browser and follow the instructions below.
First of all, arrange your equation in the standard form.
For example, if your equation is:
6 + 3x2 + 2x = -3.
Then it should be rearranged to:
3x2 + 2x + 9 = 0
When you open the calculator, you can see there are three input boxes. These fields are for entering the values of the coefficients. The first one is for A value, second is for B value, and the third is for C value. So, enter your values as per your requirements.
After filling coefficients, just press the Calculate button to start the calculation. For new calculations, you can use "Reset" button.
Finally, you will get Discriminant, First root, and Second Root as an output. Also, our calculator gives you the Quadratic Formula with entered values.
Using our online Quadratic Formula Calculator, you can easily determine the quadratic equations and roots. Also, you can learn so many things from this article with examples. Most importantly, it will give you the final results in just a few keystrokes.