The value of `b` for which the equation `2(log)_(1/(25))(b x+28)=-(log)_5(12-4x-x^2)` has coincident roots is `b=-12` (b) `b=4orb=-12` `b=4orb=-12` (d) `b=-4orb=12`

Options

A. b = - 12
B. b = 4
C. b = 4 or b =- 12
D. b =- 4 or b = 12

Answer

C

Explanation

`(2 log _(5) (bx+28))/(log_(5)(1//5)^(2))=-log_(5)(12-4x-x^(2))`
` rArr bx+28=12-4x-x^(2)`
` or x^(2)+(b+4)x+16 = 0`
For coincident roots,
D = 0
`rArr (b+4)^(2)=4(16)`
`rArr b+4 = pm 8`