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
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
Updated On: Sep 26, 2024
- 11
- 14
- 24
- 23
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The Correct Option is C
Solution and Explanation
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.
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