Enter Coefficients
ax² + bx + c = 0
x² +
x +
= 0
Quadratic Equation Calculator
Step-by-Step Solver for ax² + bx + c = 0
Quadratic Equation Calculator – Solve Quadratic Equations Step by Step
The Quadratic Equation Calculator is a powerful online math tool that helps students, teachers, and learners solve quadratic equations easily with step-by-step explanations. Quadratic equations are a fundamental part of algebra and are widely used in mathematics, physics, engineering, economics, and real-life problem solving.
What is a Quadratic Equation?
A quadratic equation is a polynomial equation of degree 2. The standard form of a quadratic equation is:
ax² + bx + c = 0
Where:
- a ≠ 0
- b and c are real numbers
- x is the variable
What is a Quadratic Equation Calculator?
A Quadratic Equation Calculator is an online tool that finds the solutions (roots) of a quadratic equation by taking values of a, b, and c. It provides accurate answers instantly along with step-by-step solutions.
This calculator is especially useful for students preparing for exams and for teachers explaining algebra concepts.
Why Use a Quadratic Equation Calculator?
- Saves time in solving equations
- Provides step-by-step explanation
- Reduces calculation errors
- Helpful for learning and revision
- Free and easy to use
Quadratic Formula
The most common method to solve quadratic equations is the quadratic formula.
x = [-b ± √(b² − 4ac)] / 2a
This formula works for all quadratic equations.
Step-by-Step Explanation Using Quadratic Formula
Step 1: Identify the values of a, b, and c
Compare the given equation with the standard form ax² + bx + c = 0.
Step 2: Substitute values into the quadratic formula
Place the values of a, b, and c into the formula.
Step 3: Calculate the discriminant
The discriminant is the part inside the square root:
D = b² − 4ac
Step 4: Find the roots
Use + and − to find two possible solutions.
Example: Solve a Quadratic Equation Step by Step
Solve the equation:
x² − 5x + 6 = 0
Step 1: Identify values
- a = 1
- b = −5
- c = 6
Step 2: Substitute into formula
x = [−(−5) ± √((−5)² − 4×1×6)] / (2×1)
Step 3: Calculate discriminant
D = 25 − 24 = 1
Step 4: Find solutions
x = (5 ± 1) / 2
x = 3 or x = 2
Quadratic Equation Calculator – Solve Quadratic Equations Step by Step
Quadratic Equation by Factorization
Some quadratic equations can be solved by factorization method, which is simpler when factors are easy to find.
Graphical Representation of Quadratic Equation
The graph of a quadratic equation is a parabola. The roots of the equation represent the points where the parabola cuts the x-axis.
Real-Life Applications of Quadratic Equations
- Physics (motion, projectile)
- Engineering calculations
- Business profit and loss models
- Architecture and construction design
- Sports and trajectory problems
Common Mistakes While Solving Quadratic Equations
- Wrong sign of b
- Incorrect calculation of discriminant
- Forgetting ± sign
Advantages of Using an Online Quadratic Equation Calculator
- Instant results
- Step-by-step learning
- Ideal for exams and homework
- Improves conceptual understanding
Frequently Asked Questions (FAQ)
Yes, the quadratic formula works for all quadratic equations.
What if the discriminant is negative?
The equation has complex roots.
Is quadratic equation calculator free?
Yes, most online calculators are free to use.
Conclusion
The Quadratic Equation Calculator – Solve Quadratic Equations Step by Step is an essential learning tool for mastering algebra. With clear steps, examples, and explanations, it simplifies complex calculations and helps build strong mathematical foundations.