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Question

If 1,2,3 are the roots of ax3+bx2+cx+d=0, then the roots of axx+bx+cx+d=0, are

A
2,3,4
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B
1,4,9
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C
2,4,6
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D
2, 3,5
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Solution

The correct option is A 1,4,9
As 1,2,3 are roots of ax3+bx2+cx+d=0
Then S1=1+2+3=6=ba
S2=1×2+1×3+2×3=11=ca
S3=1×2×3=6=da

Now axx+bx+cx+d=0xx+bax+cax+da=0
xx6x+11x6=0xx+11x=6x+6(xx+11x)2=(6x+6)2x3+121x+22x2=36x2+36+72xx314x2+49x36=0(x1)(x4)(x9)=0
Hence, the roots are 1,4,9.

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