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

• A. 11
• B. 14
• C. 24
• D. 23

Answer 1

The Correct Option is C

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.