JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
If for a posiive integer \(n\) , the quadratic equation, \(x\left( {x + 1} \right) + \left( {x + 1} \right)\left( {x + 2} \right) + .\;.\;.\; + \left( {x + \overline {n - 1} } \right)\left( {x + n} \right) = 10n\) has two consecutive integral solutions, then \(n\) is equal to:
- A \(11\)
- B \(12\)
- C \(9\)
- D \(10\)
Answer & Solution
Correct Answer
(A) \(11\)
Step-by-step Solution
Detailed explanation
\(\sum\limits_{r = 1}^n {(x + r - 1)(x + r) = 10n} \) \(\sum\limits_{r = 1}^n {({x^2} + xr + (r - 1)x + {r^2} - r) = 10n} \) \( \Rightarrow \,\sum\limits_{r = 1}^n {({x^2} + (2r - 1)x + r(r - 1) = 10n} \)…
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