If \(2\) is a root of a quadratic polynomial, which factor must be present?
Answer and explanation
Correct answer: \(x-2\)
For any polynomial, a simple root \(r\) corresponds to the linear factor \(x-r\). So if the root is \(2\), the guaranteed factor is \(x-2\). Analysis of distractors: \(x+2\) would correspond to root \(-2\); \(2x+1\) corresponds to root \(-\tfrac{1}{2}\); and \(x^2+2\) is a quadratic expression and cannot be the linear factor associated with root \(2\). Exam tip: substitute \(x=2\) into the polynomial — it must give zero if 2 is truly a root.
Frequently asked questions
What is the correct answer to this question?
\(x-2\)
Why is this the correct answer?
For any polynomial, a simple root \(r\) corresponds to the linear factor \(x-r\). So if the root is \(2\), the guaranteed factor is \(x-2\). Analysis of distractors: \(x+2\) would correspond to root \(-2\); \(2x+1\) corresponds to root \(-\tfrac{1}{2}\); and \(x^2+2\) is a quadratic expression and cannot be the linear factor associated with root \(2\). Exam tip: substitute \(x=2\) into the polynomial — it must give zero if 2 is truly a root.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
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