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If the difference of the root x2 -px + q = 0 is unity then
  • a)
    p2 - 4q = 1
  • b)
     p2 + 4q = 1
  • c)
    p2 + 4q2 = (1 + 2q)2
  • d)
    4p2 + q2 = (1 + 2p)2
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If the difference of the root x2 -px + q = 0 is unity thena)p2 - 4q = ...
Understanding the Quadratic Equation
The given quadratic equation is x² - px + q = 0. In this equation, p is the coefficient of x, and q is the constant term.
Roots of the Equation
For a quadratic equation ax² + bx + c = 0, the roots can be determined using the formula:
- Root 1 (r1) = [p + sqrt(p² - 4q)] / 2
- Root 2 (r2) = [p - sqrt(p² - 4q)] / 2
Difference of the Roots
The difference between the roots (r1 and r2) can be calculated as follows:
- Difference = r1 - r2 = [sqrt(p² - 4q)] / 2
We are given that the difference of the roots is unity (1):
- [sqrt(p² - 4q)] / 2 = 1
Setting Up the Equation
To find the relationship between p and q, we can manipulate the equation:
1. Multiply both sides by 2:
- sqrt(p² - 4q) = 2
2. Square both sides to eliminate the square root:
- p² - 4q = 4
3. Rearranging gives:
- p² - 4q = 1
Final Conclusion
Thus, we arrive at the equation:
- p² - 4q = 1
This confirms that option (a) is indeed the correct answer.
In conclusion, the condition that the difference of the roots is unity leads us to the relationship p² - 4q = 1.
Free Test
Community Answer
If the difference of the root x2 -px + q = 0 is unity thena)p2 - 4q = ...
We have x2 - px + q = 0
Now α + β = p, αβ = q
∴ α - β = 1
2α = p + 1

Now
β = p - α

and     αβ = q

p2 - 1 = 4q ⇒ p2 - 4q = 1
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If the difference of the root x2 -px + q = 0 is unity thena)p2 - 4q = 1b)p2 + 4q = 1c)p2 + 4q2 = (1 + 2q)2d)4p2 + q2 = (1 + 2p)2Correct answer is option 'A'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If the difference of the root x2 -px + q = 0 is unity thena)p2 - 4q = 1b)p2 + 4q = 1c)p2 + 4q2 = (1 + 2q)2d)4p2 + q2 = (1 + 2p)2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the difference of the root x2 -px + q = 0 is unity thena)p2 - 4q = 1b)p2 + 4q = 1c)p2 + 4q2 = (1 + 2q)2d)4p2 + q2 = (1 + 2p)2Correct answer is option 'A'. Can you explain this answer?.
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