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Three dice are thrown, the numbers appearing on them are respectively a,b,c. The chance that the roots of the quadratic equation $a x^{2} + b x + c = 0$ are.

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Real is $\frac{43}{216}$

Real and equal is $\frac{5}{216}$

Non real is $\frac{173}{216}$

Real and unequal is $\frac{38}{216}$

answer is A, B, C, D.

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Detailed Solution

For real roots $b^{2} - 4 a c \geq 0 \Rightarrow \frac{b^{2}}{a c} \geq 4$

B	(a,c)	Fav.cases
2	(1,1)	1
3	(1,1) ,(1,2), (2,1)	3
4	(1,1), (1,2), (1,3), (1,4) ,(2,2)	8
5	(1,1) ,(1,2)……..	14
6	(1,1),………(3,3), (4,5)	17
	Total	43

For real and equal $4 ac = b^{2} = perfect square (a, c) = \{(1, 1), (1, 4) (4, 1) (2, 2) (3, 3)\}$

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