If a and b are distinct positive real numbers such that `a, a_(1), a_(2), a_(3), a_(4), a_(5), b` are in A.P. , `a, b_(1), b_(2), b_(3), b_(4), b_(5), b` are in G.P. and `a, c_(1), c_(2), c_(3), c_(4), c_(5), b` are in H.P., then the roots of `a_(3)x^(2)+b_(3)x+c_(3)=0` areA. real and distinctB. real and equalC. imaginaryD. none of these

If a and b are distinct positive real numbers such that `a, a_(1), a_(

1.	If a and b are distinct positive real numbers such that `a, a_(1), a_(2), a_(3), a_(4), a_(5), b` are in A.P. , `a, b_(1), b_(2), b_(3), b_(4), b_(5), b` are in G.P. and `a, c_(1), c_(2), c_(3), c_(4), c_(5), b` are in H.P., then the roots of `a_(3)x^(2)+b_(3)x+c_(3)=0` areA. real and distinctB. real and equalC. imaginaryD. none of these
Answer» Correct Answer - C Clearly, `a_(3), b_(3) and c_(3)` are A.M., G.M. and H.M. respectively of a and b. Therefore, `b_(3)^(2)=a_(3) c_(3)` Now, Discriminant `= b_(3)^(2) - 4a_(3) c_(3) = b_(3)^(2) - 4b_(3)^(2) lt 0" "[because a_(3) c_(3) = b_(3)^(2)]` Hence, roots of the given equation are imaginary.

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