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Question

If one root is n times the other for the equation ax2+bx+c=0, then

A
nb2=ac(n+1)2
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B
n2b=ac(n+1)2
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C
(nb)2=a2c(n+1)
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D
nb=ac(n+1)
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Solution

The correct option is A nb2=ac(n+1)2
Let the roots be α, nα.
α+nα=ba
α=ba(1+n) (1)
and
αnα=ca
α2=can (2)

From (1) and (2)
b2a2(1+n)2=can
nb2=ac(n+1)2

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