A) real and equal, roots
B) real and unequal roots
C) imaginary roots
D) roots which are in A.P.
Correct Answer: C
Solution :
\[{{\alpha }_{n}}=\frac{a+b}{2},\] \[{{\beta }_{n}}\sqrt{ab},\] \[{{\gamma }_{n}}=\frac{2ab}{a+b}\] |
\[\therefore \] the equation is |
\[\frac{a+b}{2}{{x}^{2}}-\sqrt{ab}\,x+\frac{2ab}{a+b}=0\] |
its discriminant D < 0 |
\[\therefore \] the roots are imaginary |
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