Match the following-
Column-I | Column- II |
(A) If a, b, c are unequal positive numbers and is A.M. of a and c then the roots of are | (P) of opposite signs |
(B) If , then the roots of the equation (a + 1) are | (Q) rational Numbers |
(C) If are unequal positive numbers and b is H.M. of a and c then the roots of are | (R) real and unequal |
(D) If and 0 then the roots of ( are | (S) imaginary |
Text Solution
Verified by Experts(i) (ii); (iii) (iv)
Ans.
(i) 
(ii) 
(iii) 
(iv) 
Sol. (i) 
is A.M. of 
and 
⇒ The equation has real and distinct roots. Also, 
are positive so the roots are negative.
(ii) 
has roots of opposite signs.
(iii) 
is H.M. of 
and 
⇒ the equation has imaginary roots.
(iv) Discriminant of the equation is
∴ roots of equation are real and distinct. Also the product of roots 
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