A) real
B) imaginary
C) can?t say
D) None of these
Correct Answer: A
Solution :
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 \[D={{B}^{2}}-4AC\] \[={{(a+b)}^{2}}-4ab(1-ab)\] \[={{a}^{2}}+{{b}^{2}}+2ab-4ab+2{{a}^{2}}{{b}^{2}}\] \[={{(a-b)}^{2}}+{{(2ab)}^{2}}\ge 0\] Hence, roots are real.
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