If each of the coefficients a, b, c in the eq | vedclass

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(D) The equation is $ax^2 + bx + c = 0$.For the equation to have equal roots,the discriminant must be zero,i.e.,$D = b^2 - 4ac = 0$,which implies $b^2

Vedclass · Accepted Answer

$\frac{5}{216}$

Vedclass · Answer

(D) The equation is $ax^2 + bx + c = 0$.For the equation to have equal roots,the discriminant must be zero,i.e.,$D = b^2 - 4ac = 0$,which implies $b^2 = 4ac$.Since $a, b, c$ are determined by throwing a die,each can take values from the set $\{1, 2, 3, 4, 5, 6\}$. The total number of outcomes is $6 	imes 6 	imes 6 = 216$.We need to find the number of triplets $(a, b, c)$ such that $b^2 = 4ac$.$b$$(a, c)$Count$b=1$$1 = 4ac$ (No solution)$0$$b=2$$4 = 4ac \implies ac = 1 \implies (1, 1)$$1$$b=3$$9 = 4ac$ (No solution)$0$$b=4$$16 = 4ac \implies ac = 4 \implies (1, 4), (4, 1), (2, 2)$$3$$b=5$$25 = 4ac$ (No solution)$0$$b=6$$36 = 4ac \implies ac = 9 \implies (3, 3)$$1$Total favorable outcomes $= 1 + 3 + 1 = 5$.Required probability $= \frac{	ext{Favorable outcomes}}{	ext{Total outcomes}} = \frac{5}{216}$.

If each of the coefficients $a, b, c$ in the equation $ax^2 + bx + c = 0$ is determined by throwing a die,then the probability that the equation will have equal roots is:

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