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Question

Each coefficient in the equation ax2+bx+c=0 is determined by throwing an ordinary die. Find the probability that the equation will have equal roots.


A

5216

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B

3216

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C

15216

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D

1216

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Solution

The correct option is B 5216

Roots equal b24ac=0
(b2)2=ac
Each coefficient is an integer, so we consider the following cases:
If b=1
14=ac. No integral values of a and c.

If b=2
1=ac(1,1)

If b=3
92=ac No integral values of a and c.

If b=4
4=ac(1,4),(2,2),(4,1),

If b=5
252=ac, No integral values of a and c.

b=6
9=ac(3,3)
Thus we have 5 favourable ways for b=2,4,6
Total number of equations is 6×6×6=216 as each variable has 6 possible results, when a die is thrown.
Required probability is 5216


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