If \(x-a\) is a factor of a quadratic polynomial, then what is \(a\)?
Answer and explanation
Correct answer: Root
By the factor theorem, if \(x-a\) is a factor then substituting \(x=a\) into the polynomial gives value 0. Hence \(a\) is a root (zero) of the polynomial. Option A (coefficient) is incorrect because a coefficient is the multiplier of a term and does not indicate a value that makes the polynomial zero. Option D (constant term) is a different concept — the term independent of \(x\). Exam tip: plug in \(x=a\); if the polynomial evaluates to 0, then \(x-a\) is a factor.
Frequently asked questions
What is the correct answer to this question?
Root
Why is this the correct answer?
By the factor theorem, if \(x-a\) is a factor then substituting \(x=a\) into the polynomial gives value 0. Hence \(a\) is a root (zero) of the polynomial. Option A (coefficient) is incorrect because a coefficient is the multiplier of a term and does not indicate a value that makes the polynomial zero. Option D (constant term) is a different concept — the term independent of \(x\). Exam tip: plug in \(x=a\); if the polynomial evaluates to 0, then \(x-a\) is a factor.
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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