Match the following columns.
Column IColumn II(A) If are four non-zero real numbers such that andt…

Question

Match the following columns.
Column IColumn II(A) If  are four non-zero real numbers such that andthe roots of the equationare real and equal, then(P)    (B) If the equation  and  have a common real root, then(Q)     are in AP(C)    Let  be positive real numbers such that the expressionis non-negative, , then(R)     are in GP(D)    Let  be such that , then the equation has equal roots,(S)     are in HP

CGP EDU Academic Team · Accepted Answer

The correct answer is A. – (Q, R, S), – (P), – (Q), – (R)

which is possible only when

and  are in AP.

is a root of

Given, roots [Eq. (ii)] are equal.

or 
 and  are in HP…..(iii)
From Eqs. (i) and (ii), we get

and  are in  and HP.

⇒ Common root,

Given,

Hence  and  are in AP.

Now, roots are equal,

are in GP.
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	Column I		Column II
(A)	If are four non-zero real numbers such that and the roots of the equation are real and equal, then	(P)
(B)	If the equation and have a common real root, then	(Q)	are in AP
(C)	Let be positive real numbers such that the expression is non-negative, , then	(R)	are in GP
(D)	Let be such that , then the equation has equal roots,	(S)	are in HP

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