If the equation \(x^2-2ax+a^2-36=0\) is given, what is the difference between its larger and smaller roots?
Answer and explanation
Correct answer: 12
The equation can be rewritten as \((x-a)^2-36=0\). Thus, \((x-a)^2=36\), giving the roots \(x=a+6\) and \(x=a-6\). Their difference is \((a+6)-(a-6)=12\). The expression \(a+6\) represents only one root, not the difference. Exam tip: First rewrite such equations in perfect-square form.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
The equation can be rewritten as \((x-a)^2-36=0\). Thus, \((x-a)^2=36\), giving the roots \(x=a+6\) and \(x=a-6\). Their difference is \((a+6)-(a-6)=12\). The expression \(a+6\) represents only one root, not the difference. Exam tip: First rewrite such equations in perfect-square form.
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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