Text Solution
A quadratic equation is of the form ax² + bx + c = 0, where a, b, and c are constants, and a ≠ 0. To solve for x, use the quadratic formula:
x = [-b ± √(b² – 4ac)] / (2a)
The term under the square root, b² – 4ac, is the discriminant (D). It determines the nature of the roots:
- If D > 0, there are two distinct real roots.
- If D = 0, there is one real root (repeated).
- If D < 0, there are no real roots (complex roots).
Example: Solve x² – 3x + 2 = 0.
Here, a = 1, b = -3, c = 2.
Discriminant: D = (-3)² – 4*1*2 = 9 – 8 = 1 > 0.
Using the formula:
x = [3 ± √1] / 2 = [3 ± 1] / 2
x = (3 + 1)/2 = 2 or x = (3 – 1)/2 = 1.
Solutions: x = 1 and x = 2.
