let the equation $x(x+2)(12-k)=2$ have equal roots. Then the distance of the point $\left(k,\frac{k}{2}\right)$ from the line $3x+4y+5=0$ is [JEE Main 2025, 3 Apr (Shift 2)]

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let the equation \(x(x+2)(12-k)=2\) have equal roots. Then the distance of the point \(\left(k,\frac{k}{2}\right)\) from…

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