Quadratic Formula Calculator

The quadratic formula is used to solve the quadratic equation Ax2+Bx+C. A quadratic equation can be solved by other methods. These methods are

  • Factorizing

  • Completing the square

  • Graphing

The quadratic formula determines whether the discriminant b2 - 4ac is less than, greater than, or equal to 0.

  • If b2 - 4ac = 0, It shows that there is one real root.

  • If b2 - 4ac > 0, It shows that there are two real roots.

  • If b2 - 4ac < 0, It shows that there are two complex roots.

 

Formula of Quadratic Formula Calculator

The formula for the quadratic equation is

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

Note:

To calculate fractions, you can use our Fraction Calculator.

Example

Find the Solution for x2 + 4x + 0 = 0, where a = 1, b = 4 and c = 1, using the Quadratic Formula.

Solution

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

Putting the values, in the above equation we have

\[x = \frac{{ - 4 \pm \sqrt {{4^2} - 4(1)(1)} }}{{2(1)}}\] \[x = \frac{{ - 4 \pm \sqrt {16 - 4} }}{2}\] \[x = \frac{{ - 4 \pm \sqrt {12} }}{2}\] \[x = \frac{{ - 4 \pm \sqrt {4 \times 3} }}{2}\]

Here, the discriminant b2-4ac > 0, so there are two real numbers. Simplifying the equation

\[x = \frac{{ - 4}}{2} \pm \frac{{\sqrt {4 \times 3} }}{2}\] \[x = \frac{{ - 4}}{2} \pm \frac{{2\sqrt 3 }}{2}\] \[x = - 2 \pm \sqrt 3 \] \[x_1 = - 2 + \sqrt 3 \] \[x_2 = - 2 - \sqrt 3 \]

After more simplification it becomes

x1 = - 0.267 ,   x2 = - 3.732

How to use the Quadratic Formula Calculator?

The steps to use the Quadratic formula calculator are as follows:

Step 1: Enter the value of an in the first required input.

Step 2: Enter the value of b in the second required input.

Step 3: Enter the value of c in the third required input.

Step 4: The calculator will automatically display an answer on the screen.

Calculator use

Our Quadratic formula calculator is used to find the solution to quadratic equations. Quadratic equations can be solved with other methods but we preferred to solve them with quadratic equations.