JEE Main 2024 — 5 April, Shift 1 — Question 10

$a x^{2}+b x+c=0$

$\mathrm{a}, \mathrm{b}, \mathrm{c} \in\{1,2,3,4,5,6,7,8\}$

Repeated roots $\mathrm{D}=0$

$\Rightarrow \mathrm{b}^{2}-4 \mathrm{ac}=0 \Rightarrow \mathrm{~b}^{2}=4 \mathrm{ac}$

$\Rightarrow(\mathrm{a}, \mathrm{b}, \mathrm{c})$

$(1,2,1) ;(2,4,2) ;(1,4,4) ;(4,4,1) ;(3,6,3)$; $(2,8,8) ;(8,8,2) ;(4,8,4)$

8 case

Prob $=\frac{8}{8 \times 8 \times 8}=\frac{1}{64}$