What is the number of real roots of the equation (x - 1)2 + (x - 3)2 + (x - 5)2 = 0?

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
View all NDA Papers >
  1. None
  2. Only one
  3. Only two
  4. Three

Answer (Detailed Solution Below)

Option 1 : None
Free
BSF HC RO/RM All India Mega Live Test
5.4 K Users
100 Questions 200 Marks 120 Mins

Detailed Solution

Download Solution PDF

Explanation:

Given:

(x - 1)2 + (x - 3)2 + (x - 5)2 = 0

⇒ x2 – 2x + 1 + x2 – 6x + 9 + x2 – 10x + 25 = 0

⇒ 3x2 – 18x + 35 = 0

Now, discriminant D =  (–18)2 –4 × 3 × 35 

= – 96 < 0

Thus, The given equation does not have any real roots. 

∴ Option (a) is correct

Latest NDA Updates

Last updated on May 30, 2025

->UPSC has released UPSC NDA 2 Notification on 28th May 2025 announcing the NDA 2 vacancies.

-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.

->The NDA exam date 2025 has been announced for cycle 2. The written examination will be held on 14th September 2025.

-> Earlier, the UPSC NDA 1 Exam Result has been released on the official website.

-> 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. 

Get Free Access Now
Hot Links: teen patti dhani teen patti gold apk download teen patti 500 bonus teen patti game - 3patti poker teen patti joy official