In addition to this problem, I have a similar problem in my assignment asking me to find k such that $|x^2-1|+x=k$ has only one root. Proceeding similarly , I
Removed the modulus and made two different equations $x^2+x−(k+1)=0$ and $x^2−x+(k−1)=0$.
After this, I took $D_1>0$ and $D_2<0$ in the first case and $D_1<0$ and $D_2>0$ in the second. In the first case, I got $k=-5/4$ and $k>5/4$ and in the second case I got $k=5/4$ and $k<-5/4$. Where did I go wrong?
Best Answer
The most efficient method to solve this would be to draw the graphs of the function and then, by trial and error, see which value (or range of values) of $k$ satisfy the condition. For different values of k, the graph will intersect the x-axis at different points, the key is to see what values of k would satisfy the condition.