What is a quadratic equation?
Answer
A quadratic equation is a polynomial equation of degree 2 in the form ax² + bx + c = 0, where a ≠ 0.
The working
Standard form
It is written as ax² + bx + c = 0, where a, b and c are real numbers and a ≠ 0. The highest power of the variable is 2.
Number of roots
A quadratic equation always has exactly two roots, which may be real and distinct, real and equal, or complex.
Quadratic formula
The roots are given by x = [−b ± √(b² − 4ac)] ÷ 2a. This solves any quadratic equation directly.
Discriminant
The value D = b² − 4ac decides the nature of roots: D > 0 gives two real roots, D = 0 gives equal roots, and D < 0 gives complex roots.
Example
For x² − 5x + 6 = 0, factoring gives (x − 2)(x − 3) = 0, so x = 2 or x = 3.
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