What is the positive difference between the two roots of (x^2-2kx+(k^2-4)=0)?
Answer and explanation
Correct answer: (4)
The equation can be rewritten as ((x-k)^2-4=0). Thus, ((x-k)^2=4), giving the roots (x=k+2) and (x=k-2). Therefore, their positive difference is ((k+2)-(k-2)=4). Option B, 2, is the distance of each root from k, not the difference between the two roots. Exam tip: If ((x-a)^2=b^2), the roots are (a+b) and (a-b).
Frequently asked questions
What is the correct answer to this question?
(4)
Why is this the correct answer?
The equation can be rewritten as ((x-k)^2-4=0). Thus, ((x-k)^2=4), giving the roots (x=k+2) and (x=k-2). Therefore, their positive difference is ((k+2)-(k-2)=4). Option B, 2, is the distance of each root from k, not the difference between the two roots. Exam tip: If ((x-a)^2=b^2), the roots are (a+b) and (a-b).
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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