Please enter the following details
Free Daily Targets & Mocks
Study Material & Formulas PDFs
1 on 1 Mentorship
Question 93
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
Correct Answer: 24
Solution
$$f_{1}(x)=x^{2}+11x+n$$ 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, b$$^2$$-4ac>0
$$ 10^2 > 4n$$
=> n < 100/4
=> n < 25
Thus, largest integral value that n can take is 24.
Video Solution
Create a FREE account and get:
- All Quant CAT complete Formulas and shortcuts PDF
- 38+ CAT previous year papers with video solutions PDF
- 5000+ Topic-wise Previous year CAT Solved Questions for Free
CAT Quant Questions | CAT Quantitative Ability
CAT Profit, Loss and Interest QuestionsCAT Remainders QuestionsCAT Geometry QuestionsCAT Averages Mixtures Alligations QuestionsCAT Averages Questions
CAT DILR Questions | LRDI Questions For CAT
CAT Data Interpretation QuestionsCAT Selection With Condition QuestionsCAT Charts QuestionsCAT DI Miscellaneous QuestionsCAT Special Charts Questions
