What is a Quadratic equation?

Quadratic equations are secondary algebraic expressions of the form ax2 + bx + c = 0. The word Quadratic is derived from the word “Quad”, which means square. In other words, this equation is the “equation of degree 2.” One of the uses of this equation is to describe the time when a racket is launched. Quadratic equation represents an equation that appears in the form ax2 + bx + c = 0. X represents the unknown in this expression, and a, b, and c represent known numbers or coefficients. All x values that can satisfy it are called solutions. This type of formula has two solutions. If there is no real solution, there are two complex solutions. A quadratic equation consistently has two roots if complex roots are incorporated, and a twofold root is meant two.


Babylonian mathematicians take care of issues identifying with the spaces and sides of square shapes. In the present day, the issues ordinarily elaborate tackling a couple of simultaneous equations of the structure x + y = p, xy = p.

The means given by Babylonian scribes for taking care of the above square shape issue, as far as x and y, were as per the following:

1. Compute half of p
2. Square the result
3. Subtract q
4. Find the (positive) square root using a table of squares
5. Add together the results of steps (1) and (4) to give x

In modern notation this means calculating:

x = -\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}

, which today is equivalent to the modern quadratic formula for larger true roots:

x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}

, where a = 1, b = -p and c = q.

What is Quadratic Equation Calculator

A quadratic equation calculator is a calculator that solves the second-degree algebraic equations, such as ax + bx + c = 0 for x, where a ≠ 0. In doing so, CalconCalculator finds both the real and complex roots of these equations. It can also utilize other methods helpful to solving quadratic equations.

How to solve Quadratic formula in Calculator?

First of all, to say that x represents the unknown. And a, b, c represent the known numbers you enter in our calculator. Where a is not equal to 0. If a = 0, then the equation is linear, not quadratic.

All you have to do is enter the known numbers into the calculator (a, b, c) and let the calculator do all the work for you.

Quadratic formula examples

We have several types of equations, and we will list some of them:

The standard form of the equation

The easiest way to learn quadratic equations is to start with the standard form. Keep in mind that not all quadratic equations will be in this style. The first constant must not be zero.

Examples of the standard form of a quadratic equation (ax² + bx + c = 0) include:

  • 5x² + 11x – 32 = 0
  • 3x² – 3x – 1 = 0
  • -6x² – 7x +15 = 0
  • 22x² -16x – 3 = 0
  • x² -x – 2 = 0
  • 6x² – 5x – 9 = 0
  • 3x² + 3x + 2 = 0
  • -x² + 6x + 21 = 0

Incomplete Quadratic Equation Examples

As you progress your algebraic skills, you will realize that not all quadratic equations are in standard form. See a few examples of several different instances of non-standard quadratic equations.

Missing the Linear Coefficient

Sometimes a quadratic equation doesn’t have the linear coefficient or the bx part of the equation. Examples include:

  • 4x² – 34 = 0
  • x² – 16 = 0
  • 9x² + 46 = 0
  • -6x² – 4 = 0
  • 4x² + 91 = 0
  • -x² – 6 = 0
  • 3x² – 46 = 0
  • 6x² + 114 = 0

Missing the Constant Term

Quadratic equations can also lack the constant term, or c. For example:

  • 3x² – 7x = 0
  • 2x² + 8x = 0
  • -x² – 3x = 0
  • 4x² + 2x = 0
  • -5x² – 5x = 0
  • -8x² + x = 0
  • -12x² + 14x = 0
  • 13x² – 21x = 0

For what is the Quadratic formula used?

Quadratic equations are used as much as possible daily in life, calculating areas, determining profit products, or formulating the velocity of an object.

We will give a few examples of the application of this equation in everyday life.

Calculating the area of the room

People often need to calculate the area of houses, boxes, or land. An example might be making a rectangular box where one side must be twice the size of the other.

Speed calculation

The quadratic equation is also used in calculating velocity. Kayaks, for example, use the square equation to assume speed when going along a river or down a river.

Quadratic factorization

The term x – r is factor of the polynomial ax2 + bx + c if and only if r is a root of the quadratic equation ax2 + bx + c = 0. It follows the quadratic formula that:

ax^2 + bx + c = a\Bigg( x- \frac{-b-\sqrt{b^2-4ac}}{2a}\Bigg) \Bigg(x - \frac{-b-\sqrt{b^2-4ac}}{2a}\Bigg)

In the special case b2 = 4ac where the quadratic has only one distinct root (the discriminant is 0), the quadratic polynomial can be factored as

ax^2 + bx + c = a\Bigg(x+\frac{b}{2a}\Bigg)^2

Check out our linear equation calculator!