Question

The roots of $(x-a)(x-a-1)+(x-a-1)(x-a-2)+(x-a)(x-a-2)=0$, $aϵR$ are always

• A. Equal
• B. Imaginary
• C. real and distinct
• D. cannot say

Answer 1

The correct option is D cannot say

Multiplying the equation we get ;

$3x^2-x(6a+6))+a^2(a+1{)}^2(a+2{)}^2=0$

$\Rightarrow descriminant=36(a+1{)}^2-4a^2(a+1{)}^2(a+2{)}^2$

$\Rightarrow descriminant=4(a+1{)}^2(9-a^2(a+2{)}^2)$

Here the value of descriminant depends upon 'a' and we cannot say about the positivity and negativity of descriminant

Therefore we cannnot say about the nature of roots