Let the equation x(x+2)(12-k)=2 have equal roots. Then the distance of the point (k, k/2 ) from the line 3 x+4 y+5=0 is

Mathematics · Quadratic Equations

JEE Main 2025 — 3 April, Evening Shift — Question 23

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 $3 x+4 y+5=0$ is

$x^{2}+2 x-\frac{2}{12-k}=0$

$D=0$ $4-4\left(\frac{-2}{12-k}\right)=0$

$1+\frac{2}{12-k}=0$

$\Rightarrow k=14$

Point $(14,7)$

Distance $=\left|\frac{3(14)+4(7)+5}{5}\right|$

$d=15$

Option (2) is correct

Answer key and solution verified before publishing.

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