If \(x+5\) is a factor of a quadratic polynomial, which root is certain?
Answer and explanation
Correct answer: -5
If \(x+5\) is a factor, set the factor equal to zero: \(x+5=0\) gives \(x=-5\). Hence the certain root is \(-5\). Option A (5) is incorrect because the sign is reversed; solving \(x+5=0\) does not give +5. Option C (0) would only be correct if the factor were \(x\). Option D (\(\tfrac{1}{5}\)) would arise from a factor \(x-\tfrac{1}{5}\), not \(x+5\). Exam tip: always equate the linear factor to zero to find its root quickly.
Frequently asked questions
What is the correct answer to this question?
-5
Why is this the correct answer?
If \(x+5\) is a factor, set the factor equal to zero: \(x+5=0\) gives \(x=-5\). Hence the certain root is \(-5\). Option A (5) is incorrect because the sign is reversed; solving \(x+5=0\) does not give +5. Option C (0) would only be correct if the factor were \(x\). Option D (\(\tfrac{1}{5}\)) would arise from a factor \(x-\tfrac{1}{5}\), not \(x+5\). Exam tip: always equate the linear factor to zero to find its root quickly.
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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