Let `A={x:x^(2)-4x+3 lt 0,x in R }` `B={x: 2^(1-x)+p le 0 , x^(2)-2(p+7)x+5 le0}` If `B sube A`, then `p in `

Options

A. `[-4,-1]`
B. `[-4,oo)`
C. `(-oo,1)`
D. `[0,1]`

Answer

A

Explanation

`(a)` `A=(1,3)`
For `BsubeA{:(2^(1-1)+p le0,p le -1),(2^(1-3)+p le 0, p le -1//4):}}p le -1`
`f(x)=x^(2)-2(p+7)x+5`
`{:(f(1) le0 implies p ge -4),(f(3) le 0 implies pge-1):}}P ge -4`
So `p in[-4,-1]`