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Question

If the equation ax2+bx+c=0 and x3+3x2+3x+2=0 have two common roots, then


A
a = b c
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B
a b = c
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C
a = b = c
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D
a = - b = c
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Solution

The correct option is B a = b = c
x3+3x2+3x+2=0(x+1)3+1=0(x+1)=1,ω,ω2x=2,1ω,1ω2x=2,ω2,ω
Since given equations have two common roots therefore ω and ω2 are the common roots of the two equations.
Equation whose roots are ω and ω2 is x2+x+1=0
Comparing with ax2+bx+c=0, we get a1=b1=c1ie.,a=b=c.

Mathematics

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