If the equations x^2+bx-1=0 and x^2+x+b=0 have a common root different from -1, then |b| i…

Question

If the equations $x^2+bx-1=0$ and $x^2+x+b=0$ have a common root different from $-1$, then $|b|$ is equal to:

Accepted Answer

Solving simultaneously (eliminating $x$) gives $b^3+3b=0 \implies b(b^2+3)=0 \implies b^2=-3 \implies b=\pm\sqrt3i$.

$$|b|=\sqrt3.$$

Solutions · 1