Question

Determine m para que a equação mx²+(2m - 5)x + m =0 tenha raízes reais.

Answer 1

$mx^{2}+(2m-5)x+m = 0 \\\\ \text{condi\c{c}\~{a}o} \rightarrow \boxed{\Delta \geqslant 0} \\\\ \Delta = b^{2}-4 \cdot a \cdot c \\\\ (2m-5)^{2}-4 \cdot (m) \cdot (m) \geqslant 0 \\\\ 4m^{2}-20m+25-4m^{2} \geqslant 0 \\\\ -20m \geqslant -25 \\\\ \boxed{\boxed{m \leqslant \frac{5}{4}}}$