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Column IColumn II(A) If the roots of the equation(P)7x39x2+26xk=0 are positiveand in A.P., then k is equal to(B) If the roots of the equation(Q)11x314x2+kx64=0 are positiveand in G.P., then k is equal to(C) If the roots of the equation(R)246x3kx2+6x1=0 are positiveand in H.P., then k is equal to(D)The harmonic mean for the roots of(S)26equation x311x2+3x26=0 is(T)56
Which of the following is the only CORRECT combination?


Your Answer
A
(A)(Q),(B)(T),(C)(S),(D)(R)
Your Answer
B
(A)(R),(B)(S),(C)(Q),(D)(Q)
Correct Answer
C
(A)(R),(B)(T),(C)(Q),(D)(S)
Your Answer
D
(A)(Q),(B)(P),(C)(R),(D)(S)

Solution

The correct option is C (A)(R),(B)(T),(C)(Q),(D)(S)
(A)
Let the roots be ad,a,a+d
ad+a+a+d=9
a=3
So 3 is the root of the equation x39x2+26xk=0
339(3)2+26(3)k=0
k=24
(A)(R)

(B)
Let the roots be ar,a,ar
(ar)(a)(ar)=64
a=4
So 4 is the root of the equation x314x2+k64=0
4314(4)2+k(4)64=0
k=56
(B)(T)

(C)
f(x)=6x3kx2+6x1=0, here roots are in H.P.
f(1x)=x36x2+kx6=0, here the roots will be in A.P.
Let the roots be ad,a,a+d
ad+a+a+d=6
a=2
So 2 is the root of the equation x36x2+kx6=0
k=11
​​​​​​​(C)(Q)

(D)
x311x2+3x26=0
Let the roots be α,β,γ
H.M.=31α+1β+1γ=3αβγαβ+βγ+γα=26
​​​​​​​(D)(S)
 

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