JEE Main 2024 (Online) 5th April Evening ShiftQuestion 1
The coefficients $a,b,c$ in the quadratic equation $ax^{2}+bx+c=0$ are from the set $\{1,2,3,4,5,6\}$. If the probability of this equation having one real root bigger than the other is $p$, then $216p$ equals :
Probability
Solution
Distinct real roots need $b^2>4ac$. Counting: $b=3$: $ac\le2$, $3$; $b=4$: $ac\le3$, $5$; $b=5$: $ac\le6$, $14$; $b=6$: $ac\le8$, $16$. Total $38$ of $216$, so $216p=38$.