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Question

All the roots of the equation x3x2+ax+b=0 are real and distinct. If they are in A.P., then

A
a(,13)
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B
a(,13)
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C
b(19,)
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D
b(127,)
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Solution

The correct option is D b(127,)
Let x1,x2,x3 are the roots of x3x2+ax+b=0
x1+x2+x3=1
(Ad)+A+(A+d)=1, (d0)
A=13

x1x2+x2x3+x3x1=a
(Ad)A+A(A+d)+(A+d)(Ad)=a
3A2d2=a
3(13)2d2=a
a=13d2<13
a(,13)

x1x2x3=b
(Ad)A(A+d)=b
13(19d2)=b
b=d23127>127
b(127,)

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