What Is Quadratic Equation?
A quadratic equation is an equation of degree two that can be written in the standard form ax² + bx + c = 0, where a is not zero.
Examples of Quadratic Equation
1
x² - 5x + 6 = 02
2x² + 3x - 2 = 03
x² = 16Formula and Key Points
Formula / rule
x = (-b ± √(b² - 4ac)) / 2a
- The highest power of the variable is 2.
- The coefficient a cannot be zero.
- A quadratic can have two, one or no real solutions.
- The discriminant b² - 4ac helps determine the type of roots.
Why This Matters in Computer Science
Used in programming formulas, symbolic computation, constraint solving, algorithm derivations and data modelling.
Worked Example
Problem
Solve x² - 5x + 6 = 0.
- Factor the quadratic: x² - 5x + 6 = (x - 2)(x - 3).
- Set each factor equal to zero.
- x - 2 = 0 gives x = 2.
- x - 3 = 0 gives x = 3.
✓
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Final Answerx = 2 or x = 3
Linear vs Quadratic Equation
| Feature | Linear Equation | Quadratic Equation |
|---|---|---|
| Highest power | 1 | 2 |
| Example | 2x + 3 = 7 | x² - 5x + 6 = 0 |
| Graph | Straight line | Parabola |
| Typical real solutions | One | Up to two |
Related Math Terms
Quadratic Equation: Frequently Asked Questions
What is the standard form of a quadratic equation?
ax² + bx + c = 0, where a is not zero.
What is the quadratic formula?
x = (-b ± √(b² - 4ac)) / 2a.
What does the discriminant tell us?
It indicates whether the equation has two real roots, one repeated real root or two complex roots.