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Question

If α, β are the roots of the equation ax2+bx+c=0 then the equation whose roots are α+1β and β+1α is

A
acx2+(a+c)bx+(a+c)2=0
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B
abx2+(a+c)bx+(a+c)2=0
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C
acx2+(a+c)cx+(a+c)2=0
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D
None of these
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Solution

The correct option is A acx2+(a+c)bx+(a+c)2=0

CONVENTIONAL APPROACH :
Here α+β=ba and αβ=ca
If roots are α+1β,β+1α, then sum of roots are
=(α+1β)+(β+1α)=(α+β)+α+βαβ=bac(a+c)
and product =(α+1β)(β+1a)
=αβ+1+1+1αβ=2+ca+ac=2ac+c2+a2ac=(a+c)2ac
Hence required equation is given by
x2+bac(a+c)x+(a+c)2ac=0
acx2+(a+c)bx+(a+c)2=0.


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