If the (x)-axis intersections of a graph are ((0,0)) and ((b,0)), where (b\neq0), what will be the sum of the zeroes?
Answer and explanation
Correct answer: (b)
The zeroes of a polynomial are the x-coordinates of its intersections with the x-axis. The point \((0,0)\) therefore gives the zero 0, while the point \((b,0)\) gives the zero b. The condition \(b\ne0\) ensures that these are two distinct points, so both zeroes must be included in the sum.
Adding the two x-coordinates gives \(0+b=b\). Thus the sum of the zeroes is b, which is option B. The value \(b^2\) would be related to a product in some contexts, not to this sum, and \(-b\) has the wrong sign. The origin should not be ignored: although its x-coordinate is 0, it contributes 0 to the sum while still being an important zero.
Frequently asked questions
What is the correct answer to this question?
(b)
Why is this the correct answer?
The zeroes of a polynomial are the x-coordinates of its intersections with the x-axis. The point \((0,0)\) therefore gives the zero 0, while the point \((b,0)\) gives the zero b. The condition \(b\ne0\) ensures that these are two distinct points, so both zeroes must be included in the sum.
Adding the two x-coordinates gives \(0+b=b\). Thus the sum of the zeroes is b, which is option B. The value \(b^2\) would be related to a product in some contexts, not to this sum, and \(-b\) has the wrong sign. The origin should not be ignored: although its x-coordinate is 0, it contributes 0 to the sum while still being an important zero.
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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