105 LearnersLast updated on June 24th, 2025
Roots Of Quadratic Equation Calculator
Calculators are reliable tools for solving simple mathematical problems and advanced calculations like trigonometry. Whether you’re solving algebraic equations, calculating interest, or planning a project, calculators will make your life easy. In this topic, we are going to talk about roots of quadratic equation calculators.
What is Roots Of Quadratic Equation Calculator?
A roots of quadratic equation calculator is a tool to figure out the solutions or roots of a quadratic equation of the form ax² + bx + c = 0.
This calculator helps to find the values of x that satisfy the equation, making solving quadratic equations much easier and faster, saving time and effort.
How to Use the Roots Of Quadratic Equation Calculator?
Given below is a step-by-step process on how to use the calculator:
Step 1: Enter the coefficients: Input the values of a, b, and c into the given fields.
Step 2: Click on calculate: Click on the calculate button to find the roots and get the result.
Step 3: View the result: The calculator will display the roots instantly.
How to Solve Quadratic Equations?
To solve a quadratic equation, there is a standard formula called the quadratic formula.
For an equation ax² + bx + c = 0, the roots are given by: x = (-b ± √(b² - 4ac)) / (2a) The term b² - 4ac is known as the discriminant.
1. If the discriminant is positive, there are two distinct real roots.
2. If the discriminant is zero, there are two equal real roots.
3. If the discriminant is negative, there are two complex roots.
Tips and Tricks for Using the Roots Of Quadratic Equation Calculator
When we use a roots of quadratic equation calculator, there are a few tips and tricks that we can use to make it a bit easier and avoid mistakes:
- Check the coefficients carefully, especially the signs.
- Understand the nature of the roots by looking at the discriminant before calculating.
- Use proper precision for complex roots to interpret them correctly.
Common Mistakes and How to Avoid Them When Using the Roots Of Quadratic Equation Calculator
We may think that when using a calculator, mistakes will not happen. But it is possible for users to make mistakes when using a calculator.
Mistake 1
Not simplifying the equation before entering coefficients.
Ensure the equation is in the standard form ax² + bx + c = 0 before entering coefficients. Incorrect simplification can lead to incorrect results.
Mistake 2
Misinterpreting the Discriminant
Understand what the discriminant indicates about the roots. For example, a negative discriminant indicates complex roots, not real ones.
Mistake 3
Forgetting to consider complex roots
Remember that when the discriminant is negative, the calculator provides complex roots. These need to be interpreted correctly if you are expecting only real solutions.
Mistake 4
Ignoring the importance of zero coefficients
Ensure that you include zero coefficients where applicable (e.g., b=0 for ax² + c = 0). Leaving out zeros can affect the results.
Mistake 5
Entering incorrect coefficients
Double-check the coefficients you input. A small mistake can lead to a completely different and incorrect solution.
Roots Of Quadratic Equation Calculator Examples
Problem 1
Find the roots of the equation 2x² - 4x - 6 = 0.
Use the formula: x = (-b ± √(b² - 4ac)) / (2a)
Here, a=2, b=-4, c=-6.
Discriminant = b² - 4ac = (-4)² - 4(2)(-6) = 16 + 48 = 64 x = (4 ± √64) / 4 x = (4 ± 8) / 4
Roots: x = 3 or x = -1
Explanation
By calculating the discriminant and using the quadratic formula, we find the roots are 3 and -1.
Problem 2
Solve the quadratic equation x² + 6x + 9 = 0.
Use the formula: x = (-b ± √(b² - 4ac)) / (2a)
Here, a=1, b=6, c=9.
Discriminant = b² - 4ac = 6² - 4(1)(9) = 36 - 36 = 0
Roots: x = -6/2 = -3 (double root)
Explanation
The discriminant is zero, which means there is one double root, -3.
Problem 3
Find the roots of the equation 3x² - x + 2 = 0.
Use the formula: x = (-b ± √(b² - 4ac)) / (2a)
Here, a=3, b=-1, c=2.
Discriminant = b² - 4ac = (-1)² - 4(3)(2) = 1 - 24 = -23
Roots: Complex roots due to negative discriminant x = (1 ± √-23) / 6
Explanation
The discriminant is negative, which indicates complex roots.
Problem 4
Solve the equation 4x² + 12x + 9 = 0.
Use the formula: x = (-b ± √(b² - 4ac)) / (2a)
Here, a=4, b=12, c=9.
Discriminant = b² - 4ac = 12² - 4(4)(9) = 144 - 144 = 0
Roots: x = -12/8 = -1.5 (double root)
Explanation
A zero discriminant indicates a double root, which is -1.5.
Problem 5
Find the roots of the equation 5x² + 2x + 1 = 0.
Use the formula: x = (-b ± √(b² - 4ac)) / (2a)
Here, a=5, b=2, c=1.
Discriminant = b² - 4ac = 2² - 4(5)(1) = 4 - 20 = -16
Roots: Complex roots due to negative discriminant x = (-2 ± √-16) / 10
Explanation
The discriminant is negative, indicating the presence of complex roots.
FAQs on Using the Roots Of Quadratic Equation Calculator
1.How do you calculate the roots of a quadratic equation?
2.What does a negative discriminant mean?
3.Can a quadratic equation have one root?
4.How do I use a roots of quadratic equation calculator?
5.Is the roots of quadratic equation calculator accurate?
Glossary of Terms for the Roots Of Quadratic Equation Calculator
- Quadratic Equation: An equation of the form ax² + bx + c = 0.
- Discriminant: The part of the quadratic formula b² - 4ac, determining the nature of roots.
- Real Roots: Solutions of the equation when the discriminant is zero or positive.
- Complex Roots: Solutions when the discriminant is negative.
- Double Root: A repeated root occurring when the discriminant is zero.
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Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
