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If m and n are the roots of the equation (x+p)(x + q)=0, then the roots of the equation (x - m) (x - n) + k = 0 are
  • a)
    P and q
  • b)
    1/p and 1/q
  • c)
    - p and -q
  • d)
    p + q and p - q
Correct answer is option 'C'. Can you explain this answer?
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If m and n are the roots of the equation (x+p)(x + q)=0, then the root...
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If m and n are the roots of the equation (x+p)(x + q)=0, then the root...
Explanation:

Given Information:
- Roots of the equation (x + p)(x + q) = 0 are m and n.

Roots of the Quadratic Equation:
- The roots of the equation (x + p)(x + q) = 0 are -p and -q.

Expanding the Second Equation:
- Expanding (x - m)(x - n) + k = 0, we get x^2 - (m + n)x + mn + k = 0.

Using Vieta's Formulas:
- Sum of roots, m + n = -(coefficient of x)/(coefficient of x^2) = -(m + n).
- Product of roots, mn = constant term/(coefficient of x^2) = k.

Substituting the Values:
- From the given information, m + n = -(p + q) and mn = k.

Finding the Roots:
- The roots of the equation x^2 - (m + n)x + mn + k = 0 are -p - q and k. Therefore, the roots are -p - q and k.
Therefore, the correct answer is option C, which states that the roots of the equation (x - m)(x - n) + k = 0 are -p - q and k.
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If m and n are the roots of the equation (x+p)(x + q)=0, then the roots of the equation (x - m) (x - n) + k = 0 area)P and qb)1/p and 1/qc)- p and -qd)p + q and p - qCorrect answer is option 'C'. Can you explain this answer?
Question Description
If m and n are the roots of the equation (x+p)(x + q)=0, then the roots of the equation (x - m) (x - n) + k = 0 area)P and qb)1/p and 1/qc)- p and -qd)p + q and p - qCorrect answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about If m and n are the roots of the equation (x+p)(x + q)=0, then the roots of the equation (x - m) (x - n) + k = 0 area)P and qb)1/p and 1/qc)- p and -qd)p + q and p - qCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If m and n are the roots of the equation (x+p)(x + q)=0, then the roots of the equation (x - m) (x - n) + k = 0 area)P and qb)1/p and 1/qc)- p and -qd)p + q and p - qCorrect answer is option 'C'. Can you explain this answer?.
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