Question

Each coefficient in equation ax² + bx + c = 0 is obtained by throwing a dair die. Find the probability that the equation has real roots?

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Answer 1

Answer:

For real roots b2 >= 4ac

We can observedifferent cases ,

1) For a =1

If c = 1 , b can have any value from 2 to 6

If c = 2 , b can have any value from 3 to 6

If c = 3 , b can have any value from 4 to 6

If c = 4 , b can have any value from 4 to 6

If c = 5 , b can have any value from 5 to 6

If c = 6 , b can have any value from 5 to 6

2) For a = 2

If c = 1 , b can have any value from 3 to 6

If c = 2 , b can have any value from 4 to 6

If c = 3 , b can have any value from 5 to 6

If c = 4 , b can have any value 6

Similarly we can find different cases for a = 3 , 4, 5 , 6

Probability = No of outcomes in this event / Total possible outcomes

= (5 + 4 + 3 + 3 + 2 + 2 + 4 + 3+ 2+ 1+ 3+2+1+3+1+2+2)/216

= 43/216

hope that this will help you

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Step-by-step explanation: