Two number $b$ and $c$ are chosen at random with replacement from the numbers 1,2,3,4,5. What is the probability that $x 2 + b x + c = 0$ has non real roots?

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925

1625

38

1125

answer is A.

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Detailed Solution

Given, two number

b

and

c

are chosen at random with replacement from the numbers 1,2,3,4,5.
In science, an inequality is a connection that makes a non-equivalent correlation between two numbers or other numerical articulations.
It is utilized frequently to analyze two numbers on the number line by their size.
Find the expression for the inequality.
In order to have quadratic inequality positive for all values of x it should be in the form of

(x ± k) 2 + C

where c>0.
Now in given question,

x 2 + b x + c > 0

.
If we take b=9 then,

x 2 + 292 x + 922

But c cannot take more than 9.
So, this case is not possible.
Similarly for 2,3,4 and 5, no value is possible for c.
When we take b=3, c can take 3,4 and 5 because,

x 2 + 252 x + 522

Where 3,4 and 5 can be split into a sum of two numbers with values 5.25+k.
Find the values which are true of b and c.
Similarly, for b=2, c can take 5, b=3, c can take 3,4,5 b=1, c can take 2,3,4,5 b=1, c can take all 1-5.
So, the number of possibilities in favor is 1+3+5=9.
Total chances possible