Coefficient a (unitless) Enter the value for a (cannot be zero)

Coefficient b (unitless) Enter the value for b

Coefficient c (unitless) Enter the constant value for c

Quick Examples:

Two Real Roots Complex Roots

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This calculator is an estimation tool. Results should be verified with official sources for important decisions.

What Is Roots of the Quadratic Equation

The roots of the quadratic equation are the values for x that make the equation equal to zero. You can think of them as the answers to the math problem. If you draw the curve of the equation on a graph, the roots are the points where the line touches or crosses the horizontal x-axis.

How Roots of the Quadratic Equation Are Calculated

Formula

This formula works by first finding the discriminant, which is the part under the square root. The discriminant tells us if the roots are real numbers or complex numbers. If the discriminant is positive, there are two answers. If it is zero, there is one repeated answer. If it is negative, the answers involve complex numbers.

Why Roots of the Quadratic Equation Matters

Finding the roots helps you solve many kinds of problems. It is useful for finding out when an object hits the ground or for calculating areas and profits.

Why Correct Inputs Are Important

Entering the wrong numbers will give you the wrong answers. This can lead to mistakes in homework or real-world projects. Always double-check your values for a, b, and c to ensure they are correct.

For Physics Problems

In physics, these equations can model how an object moves through the air. The roots often tell you when the object starts and when it lands. This helps in understanding time and distance.

For Graphing Curves

Knowing the roots helps you draw the shape of the parabola correctly. It shows you exactly where the curve crosses the center line. This makes it easier to visualize the math problem.

For Complex Roots

Sometimes the roots are not real numbers but complex ones. This happens when the discriminant is negative. This calculator handles those cases for you so you can see the full solution.