If an integer p is chosen at random in the interval `0le ple5,` then the probality that the roots of the equation `x^(2)+px+(p)/(4)+(1)/(2)=0` are real is -

Options

A. ` (4)/(5)`
B. ` (2)/(3)`
C. ` (3)/(5)`
D. None of these

Answer

B

Explanation

`DrArrP^(2)-((p)/(4)+(1)/(2))ge0`
`(p-2)*(p+1)ge0`
`pge-1"or" pge0`
In `0leple5,` possible values of p are 2,3,4,5 Thus , probability `=(4)/(6)=(2)/(3)`