If the graph cuts the x-axis at (−2, 0) and (3, 0), then what is the product of the zeroes?
Answer and explanation
Correct answer: −6
The x-intercepts of a polynomial graph give its zeroes. From the points (−2, 0) and (3, 0), the zeroes are −2 and 3. Their product is calculated directly: (−2) × 3 = −6. Therefore option A is correct. The y-coordinate is zero for both points because they lie on the x-axis, but it is not used when multiplying the zeroes; the zeroes are the x-coordinates. Option B loses the negative sign, option C could arise from adding the zeroes instead of multiplying them because −2 + 3 = 1, and option D is not the product or sum of the given values. The graph information is sufficient without knowing the polynomial’s leading coefficient.
Frequently asked questions
What is the correct answer to this question?
−6
Why is this the correct answer?
The x-intercepts of a polynomial graph give its zeroes. From the points (−2, 0) and (3, 0), the zeroes are −2 and 3. Their product is calculated directly: (−2) × 3 = −6. Therefore option A is correct. The y-coordinate is zero for both points because they lie on the x-axis, but it is not used when multiplying the zeroes; the zeroes are the x-coordinates. Option B loses the negative sign, option C could arise from adding the zeroes instead of multiplying them because −2 + 3 = 1, and option D is not the product or sum of the given values. The graph information is sufficient without knowing the polynomial’s leading coefficient.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Geometrical meaning of the zeroes of a polynomial..
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