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The values of b for which the equation 2...

The values of b for which the equation `2log_(1/25)(bx+28)=1log_5(12-4x-x^2)` has coincident roots is/are

A

b = - 12

B

b = 4

C

b = 4 or b =- 12

D

b =- 4 or b = 12

Text Solution

Verified by Experts

The correct Answer is:
C
`(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`
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