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If \(x-9\) is a factor of a quadratic polynomial, which root is certain to be a root of the polynomial?
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Answer and explanation
Correct answer: 9
By the factor theorem, if \(x-9\) is a factor, then setting the factor equal to zero gives \(x-9=0\), so \(x=9\). Hence, 9 is certainly a root. Exam tip: a factor of the form \(x-a\) gives the root \(a\), whereas \(x+a\) gives the root \(-a\).
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
By the factor theorem, if \(x-9\) is a factor, then setting the factor equal to zero gives \(x-9=0\), so \(x=9\). Hence, 9 is certainly a root. Exam tip: a factor of the form \(x-a\) gives the root \(a\), whereas \(x+a\) gives the root \(-a\).
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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