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:

Accepted Answer

24. $f_1(x) = f_2(x) \implies x^2 + 11x + n = x \implies x^2 + 10x + n = 0$. For two distinct real roots, discriminant $D > 0$. $10^2 - 4n > 0 \implies 100 > 4n \implies n < 25$. Largest positive integer $n$ is $24$.

Distinct Real Roots Condition

Explanation

Practise this under exam conditions