JEE Mains · Maths · STD 12 - 8. Application and integration
Let \(q\) be the maximum integral value of \(p\) in \([0,10]\) for which the roots of the equation \(x ^2- px +\frac{5}{4} p =0\) are rational. Then the area of the region \(\{(x, y): 0 \leq y\) \(\left.\leq(x-q)^2, 0 \leq x \leq q\right\}\) is
- A \(243\)
- B \(25\)
- C \(\frac{125}{3}\)
- D \(164\)
Answer & Solution
Correct Answer
(A) \(243\)
Step-by-step Solution
Detailed explanation
\(x ^2- px +\frac{5 p }{4}=0\) \(D = p ^2-5 p = p ( p -5)\) \(\therefore q =9\) \(0 \leq y \leq( x -9)^2\) Area \(=\int \limits_0^9(x-9)^2 dx =243\)
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