jee-main 2023 Q82

jee-main · India · session1_30jan_shift2 Solving quadratics and applications Optimization or extremal value of an expression via completing the square

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 $\left\{(x, y): 0 \leq y \leq (x - q)^{2},\, 0 \leq x \leq q\right\}$ is
(1) 243
(2) 25
(3) $\frac{125}{3}$
(4) 164

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 $\left\{(x, y): 0 \leq y \leq (x - q)^{2},\, 0 \leq x \leq q\right\}$ is\\
(1) 243\\
(2) 25\\
(3) $\frac{125}{3}$\\
(4) 164

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