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Question

Roots of the equation x3(a+b+c)x2+(ab+bc+ca)xabc=0, if x2+2x+7=0 and ax2+bx+c=0 have a common root, where a,b,cR, can be

A
4,8,28
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B
1,2,7
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C
1,4,36
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D
None of the above
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Solution

The correct option is B 1,2,7
Equation :
x3(a+b+c)x2+(ab+bc+ca)xabc=0
x2+2x+7=0
ax2+bx+c=0
they have common root
α+β=2;+ba=+21
αβ=7=ca
b=2
a=1
c=7
a=1;b=2;c=7

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