Question

If $a,b,c$ are real and $a\ne b$, the roots of the equation $(a-b)x^2-2(a+b)x+(a-b)=0$

• A. real and equal
• B. real and unequal
• C. purely imaginary
• D. None of these

Answer 1

The correct option is B real and unequal

$The\text{given equation is}(a-b)x^2+5(a+b)x-2(a-b)=0$
$D={\left[5(a+b)\right]}^2-4(a-b)(-2(a-b))$
$=25{(a+b)}^2+8{(a-b)}^2$
$\mathrm{Sin}ceaandbarereala\ne b,so{(a-b)}^2>0and{(a+b)}^2>0$
$\therefore 8{(a-b)}^2>0........\left(i\right)$
$25{(a+b)}^2>0...........\left(ii\right)$
$adding\left(i\right)and\left(ii\right)$
$25{(a+b)}^2+8{(a-b)}^2>0$
$H\text{ence, the roots of the given equation are real and unequal}$