Question

Let $q$ be the maximum integral value of $p$ in $[0,10]$ for which the roots of the equation $x^2-p x+\frac{5}{4} p=0$ are rational Then the area of the region \left\\{(x, y): 0 \leq y \leq(x-q)^2, 0 \leq x \leq q\right\\} is

• A. 164
• B. 243
• C. $\frac{125}{3}$
• D. 25

Answer 1

Answer: (B)

243

Answer 2

x2−px+45p​=0
D=p2−5p=p(p−5)
∴q=9
0≤y≤(x−9)2

Area =0∫9​(x−9)2dx=243
So , the correct option is (B) : 243