If the real zeroes of a polynomial are written as 2, 2 and −5, what are the distinct real zeroes?
Answer and explanation
Correct answer: 2 and −5
The word distinct means that each different numerical value is listed only once. The stated zeroes are 2, 2, and −5. Although 2 occurs twice, both occurrences represent the same x-coordinate and hence the same x-axis point (2, 0); the repetition indicates multiplicity, not a new distinct zero. The value −5 gives another point, (−5, 0). Therefore the set of distinct real zeroes is {2, −5}, so option A is correct. Option C repeats 2 and lists all zero occurrences rather than distinct values. Options B and D each omit one of the two different values.
Frequently asked questions
What is the correct answer to this question?
2 and −5
Why is this the correct answer?
The word distinct means that each different numerical value is listed only once. The stated zeroes are 2, 2, and −5. Although 2 occurs twice, both occurrences represent the same x-coordinate and hence the same x-axis point (2, 0); the repetition indicates multiplicity, not a new distinct zero. The value −5 gives another point, (−5, 0). Therefore the set of distinct real zeroes is {2, −5}, so option A is correct. Option C repeats 2 and lists all zero occurrences rather than distinct values. Options B and D each omit one of the two different values.
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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