Concept 4.3
The Quadratic Formula
Source: NCERT Mathematics, Class 1010 minute lesson
Formal statement
The roots of ax² + bx + c = 0 are x = (−b ± √(b² − 4ac)) / 2a, provided b² − 4ac ≥ 0.
The intuition
The formula is completing the square done once, for every quadratic at the same time. The ± is there because a square root has two signs, which is why a quadratic can have two roots.
The long fraction bar matters. 2a divides everything above it, both −b and the square root. Divide only the root and every answer comes out wrong.
The attention
Look at the 2a: it divides the whole numerator, not just the root.
x = ( −b ± √(b² − 4ac) ) / 2a
Look hereNot here
- Look here
- 2a, which divides the whole top. 2a sits under −b and the square root together. Both parts of the numerator are divided by it.
- Not here
- The square-root part. Writing −b ± √(b² − 4ac)/2a divides only the root. It looks almost the same and gives different numbers.
- What it teaches
- In a long formula, check what each operation applies to before you calculate.