Quadratic Equation Calculator

What is an Online Quadratic Equation Calculator?

An Online Quadratic Equation Calculator is a tool designed to help solve quadratic equations. A quadratic equation is a second-degree polynomial equation of the form:

where $a$, $b$, and $c$ are constants, and $x$ represents the unknown variable. The calculator uses the quadratic formula to find the solutions (or roots) of the equation:

This formula gives two possible solutions, depending on the discriminant ($b^2 - 4ac$). The calculator simplifies this process and provides the solutions instantly.

How to Use an Online Quadratic Equation Calculator?

1. Access the Tool: Open a web browser and go to an online quadratic equation calculator.
2. Enter the Coefficients: Input the values for $a$, $b$, and $c$ in the given quadratic equation. These are the coefficients of the equation $ax^2 + bx + c = 0$.
3. Click "Solve": Press the "Solve" or "Calculate" button to find the roots of the equation.
4. View the Results: The calculator will display the two solutions for $x$, which could be real or complex numbers, depending on the discriminant.

Frequently Asked Questions-

1. What is a quadratic equation?
   A quadratic equation is a second-degree polynomial equation that can be written in the form:

   $$ax^2 + bx + c = 0$$

   where $a$, $b$, and $c$ are constants, and $x$ is the variable. It is called quadratic because the highest exponent of $x$ is 2. The solutions to the quadratic equation are called the roots.

2. What is the quadratic formula?
   The quadratic formula is a method for solving any quadratic equation. It is:

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

   This formula calculates the values of $x$ that satisfy the quadratic equation $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are the coefficients of the equation.

3. Can the calculator solve equations with complex roots?
   Yes, the quadratic equation calculator can solve equations with complex roots. If the discriminant ($b^2 - 4ac$) is negative, the calculator will provide complex solutions in the form of real and imaginary parts (e.g., $x = 2 \pm 3i$).

4. What if the quadratic equation has only one solution?
   If the discriminant ($b^2 - 4ac$) equals 0, the quadratic equation has only one real solution (a repeated root). The calculator will return this single solution for $x$.

5. Can the calculator handle decimal values for the coefficients?
   Yes, the quadratic equation calculator can handle decimal values for the coefficients $a$, $b$, and $c$. You can input fractional or decimal coefficients, and the calculator will solve the equation with precise results.