In which situation is \\(x=3)\\ called a zero of the polynomial \\(p(x))\\?
Answer and explanation
Correct answer: When \\(p(3)=0)\\
A zero of a polynomial is an x–value where the polynomial evaluates to zero: if \\(p(a)=0)\\ then \\(x=a)\\ is a zero. Thus \\(x=3)\\ is a zero exactly when \\(p(3)=0)\\. Option C is a common mix-up — a zero at \\(x=3)\\ means the graph passes through \\((3,0)\\), not \\((0,3)\\). Option D is wrong because \\(p(3)=3)\\ gives value 3, not 0. Exam tip: always verify by calculating \\(p(a)\\) and checking whether it equals 0, or look for the x–intercept \\((a,0)\\).
Frequently asked questions
What is the correct answer to this question?
When \\(p(3)=0)\\
Why is this the correct answer?
A zero of a polynomial is an x–value where the polynomial evaluates to zero: if \\(p(a)=0)\\ then \\(x=a)\\ is a zero. Thus \\(x=3)\\ is a zero exactly when \\(p(3)=0)\\. Option C is a common mix-up — a zero at \\(x=3)\\ means the graph passes through \\((3,0)\\), not \\((0,3)\\). Option D is wrong because \\(p(3)=3)\\ gives value 3, not 0. Exam tip: always verify by calculating \\(p(a)\\) and checking whether it equals 0, or look for the x–intercept \\((a,0)\\).
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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