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Q.

Let  a1>a2>a3>a4>a5>a6
P=a1+a2++a6
q=a1a3+a3a5+a5a1+a2a4+a4a6+a2a6
r=a1a3a5+a2a4a6, then the equation
2x3px2+qxr=0  has
 

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a

Two roots lies between  (a3,a5)

b

Two roots between  (a1,a3)

c

One root between  (a1,a2)

d

Two roots lies between  (a1,a4)

answer is A, C.

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Detailed Solution

x3(a1+a3+a5)x2++x3(a2+a4+a6)x2=0

(xa1)(xa3)(xa5)=(xa2)(xa4)(xa6)=0

f(a3)>0,f(a1)<0

f(a4)<0,f(a5)<0

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