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One zero of is 2. What is the other zero?

Class 10PolynomialsAlgebra — Polynomials
  • A
  • B
  • C
  • D

Step-by-Step Solution

Sum of zeroes = , so the other zero is . Check: then , and ✓. Answering reports the sum itself instead of subtracting the known zero from it.
Answer: A)

Key idea: Geometric meaning of zeros

Zeros of are exactly the **-coordinates where the graph meets the -axis**.

- **Linear** = ax + : graph is a straight line, crosses -axis ONCE → exactly 1 zero.
- **Quadratic** : graph is a parabola. Possible cases:
- Crosses -axis at 2 points → 2 distinct real zeros.
- Touches -axis at 1 point → 1 repeated zero (vertex on -axis).
- Does not meet -axis → no real zeros.
- **Cubic** + …: shape is a curve that crosses 1, 2, or 3 times → 1, 2, or 3 real zeros.

So 'find the zeros' is the algebraic version of 'find where the graph crosses the -axis'.

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