Question

# Let a,b∈R−{0} and α, β are the roots of x2+ax+b=0, then

A
1α, 1β are roots of bx2+ax+1=0
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B
α, β are roots of x2ax+b=0
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C
α2, β2 are roots of x2+(2ba2)x+b2=0
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D
αβ, βα are roots of bx2+(2ba2)x+b=0
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Solution

## The correct options are A 1α, 1β are roots of bx2+ax+1=0 B −α, −β are roots of x2−ax+b=0 C α2, β2 are roots of x2+(2b−a2)x+b2=0 D αβ, βα are roots of bx2+(2b−a2)x+b=0α, β are roots of x2+ax+b=0 ⇒α+β=−a and αβ=b A) For 1α and 1β as roots 1α+1β=−ab and 1α1β=1b ⇒ Equation is x2−(−ab)x+1b=0 ⇒bx2+ax+1=0 B) For −α and −β as roots −α−β=a and (−α)(−β)=b ⇒ Equation is x2−ax+b=0 C) For α2 and β2 as roots α2+β2=(α+β)2−2αβ=a2−2b and α2β2=b2 ⇒ Equation is x2−(a2−2b)x+b2=0 ⇒x2+(2b−a2)x+b2=0 D) For αβ and βα as roots, αβ+βα=(α+β)2−2αβαβ=a2−2bb and αββα=1 ⇒ Equation is x2−(a2−2bb)x+1=0 ⇒bx2+(2b−a2)x+b=0

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