About the Quadratic Equation Calculator
Use this calculator to find the roots of a quadratic expression with coefficients a, b and c.
How the Calculation Works
The mathematical formula used by this calculator is: x = (-b ± √(b² - 4ac)) / 2a. The discriminant determines whether the equation has real or complex roots.
Key Benefits
- Fast root calculation
- Good for algebra and exam preparation
Frequently Asked Questions
What is a quadratic equation?
A quadratic equation is a polynomial equation of degree 2, written in the standard form ax² + bx + c = 0, where a ≠ 0. The highest power of the variable is 2, which is why it is called quadratic (from the Latin for square). Examples: x² - 5x + 6 = 0 or 2x² + 3x - 2 = 0. In CBSE Class 10 Mathematics, Chapter 4 is entirely dedicated to quadratic equations and carries significant board exam weight. Use the free Quadratic Equation Calculator on AbacusHand to calculate your exact result instantly.
How do you solve ax² + bx + c = 0?
The quadratic formula is: x = (-b ± √(b² - 4ac)) / 2a. For example, x² - 5x + 6 = 0 where a=1, b=-5, c=6: discriminant = 25 - 24 = 1, so x = (5 ± 1)/2, giving x = 3 or x = 2. You can also solve by factorisation or completing the square — methods taught in CBSE Class 10. The formula method works in all cases, including when factorisation is difficult. Use the free Quadratic Equation Calculator on AbacusHand to calculate your exact result instantly.
What does the discriminant mean in a quadratic equation?
The discriminant is D = b² - 4ac. It tells you the nature of the roots before you solve: if D > 0, there are two distinct real roots; if D = 0, there is exactly one real root (repeated); if D < 0, the roots are imaginary (complex). For x² - 4x + 4 = 0: D = 16 - 16 = 0, so there is one repeated root x = 2. Understanding the discriminant is a key concept in CBSE Class 10 Chapter 4. Use the free Quadratic Equation Calculator on AbacusHand to calculate your exact result instantly.
What is the difference between real and imaginary roots?
Real roots are actual numbers on the number line. Imaginary roots involve √(-1), denoted as i. For x² + 4 = 0: x² = -4, so x = ±2i — these are imaginary roots. Real roots occur when D ≥ 0. In Class 10 CBSE, students deal only with real roots. Imaginary roots are introduced in Class 11 under the Complex Numbers chapter. In engineering, imaginary roots model oscillations, electrical circuits, and signal processing. Use the free Quadratic Equation Calculator on AbacusHand to calculate your exact result instantly.
How is the quadratic equation used in Class 10 CBSE maths?
CBSE Class 10 Chapter 4 — Quadratic Equations — is one of the highest-scoring algebra chapters. Questions include: finding roots by factorisation and formula, checking the nature of roots using the discriminant, and word problems involving area, speed-distance, and age. A typical board problem: a rectangular garden has area 96 m² and perimeter 40 m — set up a quadratic and solve for dimensions. Questions carry 3–5 marks in board exams. Use the free Quadratic Equation Calculator on AbacusHand to calculate your exact result instantly.