If \(p(x)=x^2-2x+5\), what is the value of \(p(1)\), and is \(1\) a zero of this polynomial?
Answer and explanation
Correct answer: \(4\), no
Substituting \(x=1\) gives \(p(1)=1^2-2(1)+5=1-2+5=4\). Since \(p(1)\neq 0\), \(1\) is not a zero of the polynomial. Option B incorrectly treats the value as zero, while option D ignores the contribution of the term \(-2x\). Exam tip: a number is a zero of a polynomial only when substitution makes the polynomial’s value equal to zero.
Frequently asked questions
What is the correct answer to this question?
\(4\), no
Why is this the correct answer?
Substituting \(x=1\) gives \(p(1)=1^2-2(1)+5=1-2+5=4\). Since \(p(1)\neq 0\), \(1\) is not a zero of the polynomial. Option B incorrectly treats the value as zero, while option D ignores the contribution of the term \(-2x\). Exam tip: a number is a zero of a polynomial only when substitution makes the polynomial’s value equal to zero.
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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