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If a polynomial in one variable has degree 4, which statement about its number of real zeroes is definitely true?
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Answer and explanation
Correct answer: It cannot have more than 4 real zeroes
A non-zero polynomial of degree n has at most n zeroes. Therefore, a degree-4 polynomial can have no more than four real zeroes; it need not have exactly four or even one. Exam tip: distinguish “at most” from “exactly”.
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What is the correct answer to this question?
It cannot have more than 4 real zeroes
Why is this the correct answer?
A non-zero polynomial of degree n has at most n zeroes. Therefore, a degree-4 polynomial can have no more than four real zeroes; it need not have exactly four or even one. Exam tip: distinguish “at most” from “exactly”.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Polynomials in one variable.
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