If 7 is a root of a quadratic polynomial, which factor must it have?
Answer and explanation
Correct answer: \(x-7\)
By the factor theorem, if \(r\) is a root of a polynomial, then \((x-r)\) is its factor. Here, \(r=7\), so the required factor is \((x-7)\). The factor \((x+7)\) would correspond to the root \(-7\). Exam tip: substitute the given root directly into the form \(x-r\).
Frequently asked questions
What is the correct answer to this question?
\(x-7\)
Why is this the correct answer?
By the factor theorem, if \(r\) is a root of a polynomial, then \((x-r)\) is its factor. Here, \(r=7\), so the required factor is \((x-7)\). The factor \((x+7)\) would correspond to the root \(-7\). Exam tip: substitute the given root directly into the form \(x-r\).
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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