- A5
- B8
- C−2
- D3
Step-by-Step Solution
Product of zeroes = . Setting gives , so . Answering −2 solves ; 5 treats the leading coefficient as instead of ; and would make the term vanish, so the expression would not even be a quadratic.
Answer: B) 8
If the product of the zeroes of is 1, find .
Class 10PolynomialsAlgebra — Polynomials
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'.
- **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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