Question

If $x^2+px+1$ is a factor of the expression $a{x}^3+bx+c$, then

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Given that $x^2+px+1$ is factor of $a{x}^3+bx+c=0$, then

let $a{x}^3+bx+c=(x^2+px+1)(ax+\lambda )$, 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 = -$\frac{\lambda }{a}=\frac{c}{a}$

Hence b = $(-\frac{c}{a})c+aorab=a^2-c^2$