Question

$x^2+x+1$ is a factor of a $x^3+b{x}^2+cx+d=0$, the the real root of above equation is $(a,b,c,dϵR)$.

• A. $-d/a$
• B. $d/a$
• C. $(b-a)/a$
• D. $(a-b)/a$

Answer 1

The correct option is A $-d/a$

$x^2+x+1=0rootsarew,w^2{ax}^3+{bx}^3+cx+d=0hasrootsw,w^{2}letotherrootbe\alpha \therefore \alpha .w.w^2=\frac{-d}{a}\alpha w^3=\frac{-d}{a}\alpha =\frac{-d}{a}[w^3=1]$