Question
Download Solution PDFWhat is the probability that the roots of the equation x2 + x + n = 0 are real, where n ∈ ℕ and n < 4?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Consider the quadratic equation ax2 + bx + c = 0
Discriminant (D): D = b2 - 4ac
For real root: D ≥ 0
b2 - 4ac ≥ 0
Calculation:
Given equation
x2 + x + n = 0
Finding discriminant: (1)2 - 4n ≥ 0
1 ≥ 4n
n ≤ \(\rm \frac{1}{4}\)
There is no value which belongs in 1, 2, 3, ..... (i.e. natural number)
This is possible for n = 0
∴ The probability of the required event is zero.
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.