If \(p(x)=x^2-9\), which of the following numbers is not a zero of \(p(x)\)?
Answer and explanation
Correct answer: 0
A number is a zero of a polynomial only when the value of the polynomial at that number is 0. Here, \(p(3)=3^2-9=0\) and \(p(-3)=(-3)^2-9=0\), so 3 and -3 are zeros. However, \(p(0)=0^2-9=-9\neq 0\); therefore, 0 is not a zero. Exam tip: Use \(x^2-a^2=(x-a)(x+a)\) to find the zeros quickly.
Frequently asked questions
What is the correct answer to this question?
0
Why is this the correct answer?
A number is a zero of a polynomial only when the value of the polynomial at that number is 0. Here, \(p(3)=3^2-9=0\) and \(p(-3)=(-3)^2-9=0\), so 3 and -3 are zeros. However, \(p(0)=0^2-9=-9\neq 0\); therefore, 0 is not a zero. Exam tip: Use \(x^2-a^2=(x-a)(x+a)\) to find the zeros quickly.
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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