If `ain[-20, 0]`, find the probability that the graph of the function `y=16x^2+8(a+5)x-7a-5` is strickly above the X-axis.

Options

A. `(17)/(20)`
B. `(13)/(20)`
C. `(7)/(20)`
D. `(3)/(20)`

Answer

B

Explanation

If the equation `16x^(2)+8(a+5)x-7a-5=0` has imaginary roots, then
Discriminant `lt 0`
`implies 64(a+5)^(2) +64(71+5) lt 0`
`implies a^(2)+17a+30 lt 0 implies (a+15)(a+2) lt 0 implies -15 lt a lt -2`
Hence, required probability `=(underset(-15)overset(-2)intdx)/(underset(-20)overset(0)intdx)=(13)/(20)`