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Question

If x2+px+1 is a factor of the expression ax3+bx+c, then


A

a2+c2ab=0

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B

a2c2=ab

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C

a2+c2=ab

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D

a2c2=ab

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Solution

The correct option is B

a2c2=ab


Given that x2+px+1 is factor of ax3+bx+c=0, then

let ax3+bx+c=(x2+px+1)(ax+λ), where λ is a costant. Then equating the coefficient of like powers of x on both sides, we get

0=ap+λ,b=pλ+a,c=λ

p=λa=ca

Hence b = (ca)c+a
ab=a2c2


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