If α and β, α > β, are the zeroes of the polynomial p (x) = 2x2 - 5x + k such that \(\rm \alpha-\beta=-\frac{7}{2}\)then k is a zero of which of the following polynomials? 

This question was previously asked in
AAI Junior Assistant (Fire Service) Official Paper (Held On: 15 Nov 2022 Shift 1)
View all AAI Junior Assistant Papers >
  1. x2 - 2x + 3
  2. x2​ + 3x - 2
  3. x2​ + 2x - 3
  4. x2​ - 3x + 2

Answer (Detailed Solution Below)

Option 3 : x2​ + 2x - 3
Free
ST 1: English
2.3 K Users
20 Questions 20 Marks 25 Mins

Detailed Solution

Download Solution PDF

Given:

Polynomial: p(x) = 2x2 - 5x + k

Zeroes: α and β, α > β

α - β = -7/2

Formula used:

Sum of zeroes: α + β = -b/a

Product of zeroes: αβ = c/a

Calculation:

Sum of zeroes: α + β = 5/2

Given that, α - β = -7/2

⇒ (α + β) + (α - β) = 5/2 - 7/2

⇒ 2α = -1 ⇒ α = -1/2

⇒ β = 5/2 - (-1/2) ⇒ β = 3

Product of zeroes: αβ = -1/2 × 3

⇒ -3/2 = k/2

⇒ k = -3

k is a zero of the polynomial x2 + 2x - 3

∴ The correct answer is option (3).

Latest AAI Junior Assistant Updates

Last updated on Apr 24, 2025

-> The AAI Junior Assistant Response Sheet 2025 has been out on the official portal for the written examination.

-> AAI has released 168 vacancies for Western Region. Candidates had applied online from 25th February to 24th March 2025.

-> A total number of 152 Vacancies have been announced for the post of Junior Assistant (Fire Service) for Northern Region.

-> Eligible candidates can apply from 4th February 2025 to 5th March 2025. 

-> Candidates who have completed 10th with Diploma or 12th Standard are eligible for this post.

-> The selection process includes a Computer Based Test, Document Verification, Medical Examination (Physical Measurement Test), Driving Test and a Physical Endurance Test.

-> Prepare for the exam with AAI Junior Assistant Previous year papers.

Get Free Access Now
Hot Links: teen patti cash teen patti classic online teen patti teen patti gold apk teen patti star