Quadratic Equation Solver
Solve any quadratic equation of the form ax² + bx + c = 0. Enter coefficients a, b, and c to get roots, discriminant, nature of roots, vertex, and step-by-step solution.
Enter Coefficients
Roots of the Equation
x₁ = 3, x₂ = 2
Discriminant D = 1
Nature of Roots
Two distinct real roots (D > 0)
Discriminant (D)
1
D = b² − 4ac = 25 − 24
Sum of Roots (−b/a)
5
Product of Roots (c/a)
6
Vertex
(2.5, -0.25)
Parabola opens upward
Need help with your studies?
Super Tutor gives you chapter summaries, revision notes, practice quizzes, and flashcards — tailored to your board and syllabus.
Try Super Tutor — It's FreeHow to Solve a Quadratic Equation
Step 1: Write the equation in standard form: ax² + bx + c = 0
Step 2: Calculate the discriminant: D = b² − 4ac
Step 3: Apply the quadratic formula to find roots
Example: x² − 5x + 6 = 0 → a=1, b=−5, c=6
- D = (−5)² − 4(1)(6) = 25 − 24 = 1
- x = (5 ± √1) / 2 = (5 ± 1) / 2
- x₁ = 3, x₂ = 2
Frequently Asked Questions
What is the quadratic formula?
The quadratic formula is x = (−b ± √(b² − 4ac)) / 2a. It gives the roots (solutions) of any quadratic equation ax² + bx + c = 0, where a ≠ 0.
What does the discriminant tell us?
The discriminant D = b² − 4ac determines the nature of roots. If D > 0, the equation has two distinct real roots. If D = 0, it has two equal real roots (one repeated root). If D < 0, it has two complex (imaginary) roots.
How do I solve quadratic equations for CBSE Class 10?
In CBSE Class 10 Maths Chapter 4, you learn three methods: factorisation, completing the square, and the quadratic formula. For board exams, show all steps — write the standard form, calculate the discriminant, then apply the formula.
Can quadratic equations have complex roots?
Yes. When the discriminant (b² − 4ac) is negative, the roots are complex numbers involving i (the imaginary unit, where i² = −1). This is covered in Class 11 Maths (Complex Numbers chapter) and is important for JEE preparation.