Find the set of values of k, where k is a constant, when equation x^3 - 12x^2 + 45x -34 = k has one root and three roots.
Please explain in detail. Thanks.
$\displaystyle k$ will be the vertical translation applied to $\displaystyle x^3 - 12x^2 + 45x -34 $ which changes the number of roots. First thing to do is find the stationary points of this function.
Find the max and min's of the function by substituting these values into the equation. After plotting the funcrtion you will see these results shoudl act as your range for k.