If p and q are chosen randomly from the set [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] with replacement, then the probability that the roots of the equation  $x^2+px+q=0$

Roots of  $x^2+px+q=0$ will be real if $p^2\ge 4q$ 
 The possible selections are as follows.
 P                  q
 1.                  -
 2                  1
 3                  1, 2
 4                  1, 2, 3, 4
5                   1, 2, 3, 4, 5, 6
6                   1, 2, …., 9
7                   1, 2, …., 10
8                   1, 2, …., 10
9                   1, 2, …., 10
10                1, 2, …., 10
Total 62
Therefore, number of favorable ways is 62 and total number of ways is 102 = 100
 Hence, the required probability is 62/100
The roots are imaginary 1-31/50
The roots are equal 3/100
The roots are real and distinct 59/100