- A
- B
- C
- D
Step-by-Step Solution
The -intercepts give the zeroes −3 and 2, so . Sum of zeroes = forces ; writing loses that minus sign. The last option has the same zeroes but , so its parabola opens downward.
Answer: A)
A parabola opens upward and crosses the -axis at (−3, 0) and (2, 0). Which of these could be?
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'.
Master this chapter in 30 minutes a day.
Don't just memorise the answer — build a daily practice habit.
Practice 5 Similar Questions Free →All Polynomials practice questions
More Class 10 Polynomials practice
The graph of a polynomial y = p(x) meets the x-axis at 2 points and the y-axis at 1…The graph of y = ax² + bx + c opens downward and lies entirely below the x-axis. Which…The graph of a cubic polynomial cuts the x-axis at exactly one point. How many real…If α and β are the zeroes of 5x² + 3x − 2, find α + β.For 2x² + 7x + 5, the sum of the zeroes and the product of the zeroes are respectively…