Question

Roots of the equation $(x-a)\text{ (}x-b)=ab{x}^2$ are

• A. real
• B. imaginary
• C. can?t say
• D. None of these

Answer 1

Answer: (A)

Given equation is
$(x-a)(x-b)=ab{x}^2$
$\Rightarrow$ $x^2-(a+b)x+ab=ab{x}^2$
$\Rightarrow$ $(1-ab)x^2-(a+b)x+ab=0$
Discriminant $D=B^2-4AC$
$={(a+b)}^2-4ab(1-ab)$
$=a^2+b^2+2ab-4ab+2a^2{b}^2$
$={(a-b)}^2+{(2ab)}^2\ge 0$
Hence, roots are real.