Coefficients a,b,c of ax^2+bx+c=0 are obtained by throwing a die three times.

Question

Coefficients $a,b,c$ of $ax^2+bx+c=0$ are obtained by throwing a die three times. Find the probability the equation has equal roots.

Accepted Answer

$n(S)=216$. Need $b^2=4ac$. Valid $(a,b,c)$: $b=2\Rightarrow(1,1)$; $b=4\Rightarrow(1,4),(4,1),(2,2)$; $b=6\Rightarrow(3,3)$. Total: 5.

$$P = \frac{5}{216}$$

Solutions · 1