Quantitative Aptitude Question on Number Systems

Question

If $f_1 (x) = x^2 + 11x + n$ and $f_2 (x) = x,$ then the largest positive integer n for which the equation $f_1 (x) = f_2 (x)$ has two distinct real roots, is

Answer 1

Solution

The equation $x^2+11x+n=x$ can be rearranged as $x^2+10x+n=0.$
When $x^2+10x+25=0$ , the roots are real and equal.
However, for $x^2+10x+n=0$ where $n>25$ , the roots become complex.

To find the maximum value of n for which the equation has two distinct real roots, it is 24.