An object is thrown upwards with an initial velocity of $17 \mathrm{m}/\sec$ from a building with $12 \mathrm{m}$ height. It is at a height of $S=12+17t–5t^2$ from the ground after a flight of $‘t’$ seconds. Find the time taken by the object to touch the ground.

Find the nature of the roots of the following quadratic equation. If real roots exist, find them:

$2x^2-3x+5=0$

Find the nature of the roots of the following quadratic equation. If real roots exist, find them:

$3x^2-4\sqrt{3}x+4=0$

Find the nature of the roots of the following quadratic equation. If real roots exist, find them:

$2x^2-6x+3=0$

Find the values of $k$ for the following quadratic equation, so that they have two equal roots:

$2x^2+kx+3=0$

Find the values of $k$ for each of the following quadratic equations, so that they have two equal roots

$kx(x-2)+6=0(k\ne 0)$