Question

find the nature of roots log base 2(x-3)+log base
2(1-x)

Answer 1

Answer:

Step-by-step explanation:

Log(x-3)+Log(1-x)=0

Log{(x-3)×(1-x)}=0

Log{(x-3)×(1-x)}=Log1

(X-3)×(1-x)=1

X-x^2-3+3x-1=0

-x^2+4x-1=0

X^2-4x+1=0

X=[-(-4)+-√{(-4)^2-4×2×-1}]/2×1

=[4+-√16+8]/2

=[4+-√24]/2

=[4+-2√6]/2

=2+-√6

Hence,roots are (2+√6,2-√6).