Question
Download Solution PDFIf 5 lies between the roots of the quadratic equation x2 + 2(k - 3)x + 9 = 0, find the complete solution set of k.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFLet the two roots be a and b.
Given: a < 5 < b
So, from the above diagram, we can conclude that D > 0 and F(5) < 0.
F(5) < 0
52 + 2(k - 3)5 + 9 < 0
25 + 10k – 30 + 9 < 0
10k + 4 < 0
k < (- 4)/10
So,
k ε (- ∞, (- 4)/10)Last updated on Jul 8, 2025
->UPSC NDA Application Correction Window is open from 7th July to 9th July 2025.
->UPSC had extended the UPSC NDA 2 Registration Date till 20th June 2025.
-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.
->The NDA exam date 2025 has been announced. The written examination will be held on 14th September 2025.
-> The selection process for the NDA exam includes a Written Exam and SSB Interview.
-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100.
-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential.