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  4. The value(s) of 'b' for which the equation, 2 log 1 / 25(b x+28)=- log 5(12-4 x-x2) has coincident roots, is/are -

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Q. The value(s) of 'b' for which the equation, $2 \log _{1 / 25}(b x+28)=-\log _5\left(12-4 x-x^2\right)$ has coincident roots, is/are -

Complex Numbers and Quadratic Equations

Solution:

$\log _{\frac{1}{5}}(b x+28)=\log _{\frac{1}{5}}\left(12-4 x-x^2\right) $
$\Rightarrow b x+28=12-4 x-x^2$
$ x^2+(b+4) x+16=0 $
$\Rightarrow \text { since } D=0 (b+4)^2-64=0 $
$\Rightarrow b=4,-12$
$\text { At } b=-12, x=4$
Put in log domain $\Rightarrow$ No solution
at $b=4$ satisfies the domain