PrepRung
Sign inSign up free

NDA 2020 Maths · Mathematics · Quadratic Equations · medium

If the roots of x^2-6x+k=0 differ by 2, then k equals

Single correct option

If the roots of x2−6x+k=0x^2-6x+k=0 differ by 2, then kk equals
  1. A. 9
  2. B. 5
  3. C. 8
  4. D. 7
Show answer and solution

Answer: (C) 8

Let the roots be α,α+2\alpha,\alpha+2. Their sum is 66, so α=2\alpha=2 and the roots are 2 and 4. The product gives k=8k=8. Alternatively (α−β)2=36−4k=4(\alpha-\beta)^2=36-4k=4 gives k=8k=8. The value 9 corresponds to equal roots.
Report a mistake

Original question written in the NDA 2020 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake