- A2
- B
- C−2
- D6
Step-by-Step Solution
For a cubic, αβγ = . Answering 2 drops the minus sign in −/a; uses , which is the sum of the products taken two at a time, not the product of all three.
Answer: C) −2
Find the product of all three zeroes of .
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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