If a polynomial graph cuts the x-axis at (−4, 0), (2, 0), and (9, 0), what is the product of these zeroes?
Answer and explanation
Correct answer: −72
The governing concept is that every x-axis intersection (r, 0) identifies r as a real zero of the polynomial. From the three given points, the zeroes are −4, 2, and 9. Their product is (−4) × 2 × 9 = −8 × 9 = −72. Thus option B is correct. The result must be negative because exactly one of the three factors is negative; multiplying one negative factor by positive factors gives a negative product. Option A has the right absolute value but loses the sign. Option C, 7, is the sum −4 + 2 + 9, not the product. Option D, −11, is not obtained by the required multiplication. The second coordinate, 0, only confirms that the points lie on the x-axis and is not multiplied.
Frequently asked questions
What is the correct answer to this question?
−72
Why is this the correct answer?
The governing concept is that every x-axis intersection (r, 0) identifies r as a real zero of the polynomial. From the three given points, the zeroes are −4, 2, and 9. Their product is (−4) × 2 × 9 = −8 × 9 = −72. Thus option B is correct. The result must be negative because exactly one of the three factors is negative; multiplying one negative factor by positive factors gives a negative product. Option A has the right absolute value but loses the sign. Option C, 7, is the sum −4 + 2 + 9, not the product. Option D, −11, is not obtained by the required multiplication. The second coordinate, 0, only confirms that the points lie on the x-axis and is not multiplied.
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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