The number of real values of the parameter k | vedclass

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Question

(b) Let ${\log _{16}}x = y \Rightarrow {y^2} - y + {\log _{16}}k = 0$

This quadratic equation will have exactly one solution if its discriminant va

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(b) Let ${\log _{16}}x = y \Rightarrow {y^2} - y + {\log _{16}}k = 0$

This quadratic equation will have exactly one solution if its discriminant vanishes.

$	herefore {( - 1)^2} - 4.1.{\log _{16}}k = 0 \Rightarrow 1 = {\log _{16}}{k^4}$

$ \Rightarrow $${k^4} = 16$ $ \Rightarrow $ ${k^2} = 4$ $ \Rightarrow $ $k = \pm 2$.

But ${\log _{16}}k$ is not defined $k < 0$, $k = 2$.

$	herefore$ Number of real values of $k = 1$.

The number of real values of the parameter $k$ for which ${({\log _{16}}x)^2} - {\log _{16}}x + {\log _{16}}k = 0$ with real coefficients will have exactly one solution is

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