Let 0 be in R.

Question

Let $\lambda
e0$ be in $\mathbb R$. If $\alpha,\beta$ are roots of $x^2-x+2\lambda=0$ and $\alpha,\gamma$ are roots of $3x^2-10x+27\lambda=0$, then $\dfrac{\beta\gamma}\lambda$ is equal to

Accepted Answer

(Same setup as before.) Eliminating the common root $\alpha$ gives $\alpha=3\lambda$, then $\beta=\dfrac23$, $\lambda=\dfrac19$, $\gamma=3$.

$$\frac{\beta\gamma}\lambda=\frac{\frac23\cdot3}{\frac19}=18.$$

Solutions · 1