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

Question 27:
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: 24
Explanation:

$f_{1}(x)=x^{2}+11x+n$ and $f_{2}(x) = x$
$f_{1}(x)=f_{2}(x)$
=> $x^{2}+11x+n = x$
=> $ x^2 + 10x + n = 0 $
=> For this equation to have distinct real roots
$ 10^2 > 4n$
=> n < 100/4
=> n < 25
Thus, largest integral value that n can take is 24.

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CAT 2017 [slot 1] Question with solution 27

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