Let p,q,r R and rp0.

Question

Let $p,q,r\in\mathbb R$ and $r>p>0$. If the quadratic equation $px^2+qx+r=0$ has two complex roots $\alpha$ and $\beta$, then $|\alpha|+|\beta|$ is

Accepted Answer

Since coefficients are real and roots complex, $\beta=\bar\alpha$, so $|\alpha|=|\beta|=\sqrt{r/p}>1$ (as $r>p>0$).

$$|\alpha|+|\beta|=2|\alpha|>2.$$

Solutions · 1