If \(x^2-2ax+a^2-49=0\), what is the difference between the two roots of this quadratic equation?
Answer and explanation
Correct answer: 14
Complete the square: \(x^2-2ax+a^2-49=(x-a)^2-49=0\). So \((x-a)^2=49\) and the roots are \(a+7\) and \(a-7\). Their difference is \((a+7)-(a-7)=14\). Option B (7) is incorrect — it is half the actual difference. Option C (2a) is unrelated to the difference here (it would be a mistaken use of coefficients), and option D (a+7) is just one root, not the difference. Exam tip: try completing the square or factor as \((x-a-7)(x-a+7)=0\) to read off roots quickly.
Frequently asked questions
What is the correct answer to this question?
14
Why is this the correct answer?
Complete the square: \(x^2-2ax+a^2-49=(x-a)^2-49=0\). So \((x-a)^2=49\) and the roots are \(a+7\) and \(a-7\). Their difference is \((a+7)-(a-7)=14\). Option B (7) is incorrect — it is half the actual difference. Option C (2a) is unrelated to the difference here (it would be a mistaken use of coefficients), and option D (a+7) is just one root, not the difference. Exam tip: try completing the square or factor as \((x-a-7)(x-a+7)=0\) to read off roots quickly.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
