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If \(x^2-2ax+a^2-25=0\), what is the difference between the larger and smaller roots?
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Answer and explanation
Correct answer: 10
The equation can be rewritten as \((x-a)^2-25=0\). Thus, \((x-a)^2=25\), giving the roots \(a+5\) and \(a-5\). Therefore, the difference between the larger and smaller roots is \((a+5)-(a-5)=10\). In such questions, completing the square is the quickest method.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
The equation can be rewritten as \((x-a)^2-25=0\). Thus, \((x-a)^2=25\), giving the roots \(a+5\) and \(a-5\). Therefore, the difference between the larger and smaller roots is \((a+5)-(a-5)=10\). In such questions, completing the square is the quickest method.
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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