If the equation \(x^2-2ax+a^2-9=0\) is given, what is the difference between the larger and smaller roots?
Answer and explanation
Correct answer: 6
The equation can be rewritten as \((x-a)^2-9=0\). Thus, \((x-a)^2=9\), giving the roots \(x=a+3\) and \(x=a-3\). The difference between the larger and smaller roots is \((a+3)-(a-3)=6\). Option D represents only one root, while option C is not generally the difference between the roots. Exam tip: For this form, complete the square and identify the two roots directly.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
The equation can be rewritten as \((x-a)^2-9=0\). Thus, \((x-a)^2=9\), giving the roots \(x=a+3\) and \(x=a-3\). The difference between the larger and smaller roots is \((a+3)-(a-3)=6\). Option D represents only one root, while option C is not generally the difference between the roots. Exam tip: For this form, complete the square and identify the two roots directly.
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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