If a graph cuts the x-axis at (−2, 0), (3, 0), and (7, 0), what is the product of the zeroes?
Answer and explanation
Correct answer: −42
The governing concept is that the x-coordinate of every x-axis intersection is a zero of the polynomial. The three zeroes are therefore −2, 3, and 7. Their product is calculated using only the x-values: (−2) × 3 × 7 = (−6) × 7 = −42. Thus option B is correct. The negative sign is essential because there is one negative factor and two positive factors, so the final product is negative. Option A has the correct magnitude but the wrong sign. Option C is the sum of the three zeroes, since −2 + 3 + 7 = 8, not their product. Option D does not result from multiplying the listed zeroes. The y-coordinate 0 is not included in the product.
Frequently asked questions
What is the correct answer to this question?
−42
Why is this the correct answer?
The governing concept is that the x-coordinate of every x-axis intersection is a zero of the polynomial. The three zeroes are therefore −2, 3, and 7. Their product is calculated using only the x-values: (−2) × 3 × 7 = (−6) × 7 = −42. Thus option B is correct. The negative sign is essential because there is one negative factor and two positive factors, so the final product is negative. Option A has the correct magnitude but the wrong sign. Option C is the sum of the three zeroes, since −2 + 3 + 7 = 8, not their product. Option D does not result from multiplying the listed zeroes. The y-coordinate 0 is not included in the product.
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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