Distinct
Distinct
Different. Not identical.
Example
Problem: The equation x² − 5x + 6 = 0 has two solutions. Are they distinct?
Step 1: Factor the quadratic.
x2−5x+6=(x−2)(x−3)=0
Step 2: Find the solutions.
x=2orx=3
Step 3: Compare the two solutions. Since 2 ≠ 3, they are not the same value.
Answer: Yes, the equation has two distinct solutions: x = 2 and x = 3.
Why It Matters
The word 'distinct' appears constantly in math problems and theorems. For example, a quadratic equation can have two distinct real roots, one repeated root, or no real roots — and these are fundamentally different situations. Recognizing whether values are distinct also matters when counting: the set {3, 5, 7} has three distinct elements, while the list {3, 5, 5, 7} has only three distinct values even though it contains four entries.
Common Mistakes
Mistake: Confusing the number of solutions with the number of distinct solutions.
Correction: A repeated root like x = 4 in (x − 4)² = 0 counts as one distinct solution, even though it has multiplicity two. Always check whether the values are actually different from each other.
Related Terms
- Equal — Distinct means values are not equal
- Set — Sets contain only distinct elements
- Unique — Closely related meaning: one of a kind
- Quadratic Equation — Often asks for distinct real roots