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Question

The equation ax2+bx+c=0,bx2+cx+a=0 have a common root then a3+b3+c3abc

A
1
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B
3
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C
2
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D
4
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Solution

The correct option is B 3

We have,

ax2+bx+c=0 and bx2+cx+a=0 have a common root

Then,

ax2+bx+c=bx2+cx+a=0


If put x=1 then,

a+b+c=a+b+c=0

So,

a3+b3+c33abc=a3+b3+c3+3abc3abc3abc

Using formula,

a3+b3+c33abc=(a+b+c)(a2+b2+c2abbcca)


Then,

a3+b3+c33abc=a3+b3+c33abc3abc+3abc3abc

=(a+b+c)(a2+b2+c2abbcca)3abc+3

=03abc+3

=3


Hence, this is the answer.


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