The coefficients a, b, c in the quadratic equ | vedclass

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(B) For the quadratic equation $ax^2 + bx + c = 0$ to have two distinct real roots,the discriminant $D$ must be greater than $0$.$D = b^2 - 4ac > 0$,w

Vedclass · Accepted Answer

$38$

Vedclass · Answer

(B) For the quadratic equation $ax^2 + bx + c = 0$ to have two distinct real roots,the discriminant $D$ must be greater than $0$.$D = b^2 - 4ac > 0$,which implies $b^2 > 4ac$.The total number of possible outcomes for $(a, b, c)$ is $6 	imes 6 	imes 6 = 216$.We count the favorable cases where $b^2 > 4ac$:- If $b=1$: $1 > 4ac$ (No solution)- If $b=2$: $4 > 4ac \implies ac - If $b=3$: $9 > 4ac \implies ac - If $b=4$: $16 > 4ac \implies ac - If $b=5$: $25 > 4ac \implies ac - If $b=6$: $36 > 4ac \implies ac Total favorable cases $= 3 + 5 + 14 + 16 = 38$.Thus,$p = \frac{38}{216}$.Therefore,$216p = 38$.

The coefficients $a, b, c$ in the quadratic equation $ax^2 + bx + c = 0$ are chosen from the set $\{1, 2, 3, 4, 5, 6\}$. If the probability of this equation having two distinct real roots is $p$,then $216p$ equals:

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