If the equation \(x^2-2ax+a^2-16=0\) is given, what is the difference between its roots?
Answer and explanation
Correct answer: 8
The equation can be rewritten as \((x-a)^2-16=0\). Thus, \((x-a)^2=16\), giving the roots \(x=a+4\) and \(x=a-4\). Their difference is \((a+4)-(a-4)=8\). The value 4 represents the distance of each root from \(a\), not the distance between the two roots. In the exam, completing the square is a quick method for such questions.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The equation can be rewritten as \((x-a)^2-16=0\). Thus, \((x-a)^2=16\), giving the roots \(x=a+4\) and \(x=a-4\). Their difference is \((a+4)-(a-4)=8\). The value 4 represents the distance of each root from \(a\), not the distance between the two roots. In the exam, completing the square is a quick method for such questions.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
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