Question

Calcule o valor de m na equação 3x²-mx+18=0 de modo que uma de suas raízes seja 2.

Answer 1

Substitua x por 2 e calcule m:

$3.2^2-2m+18=0\\ \\ 12-2m+18=0\\ \\ 2m=12+18\\ \\ 2m=30\\ \\ m=15$

Answer 2

$3x^2-mx+18=0$

$\Delta=(-m)^2-4\cdot3\cdot18=m^2-216$

$x=\dfrac{-(-m)\pm\sqrt{m^2-216}}{2\cdot3}=\dfrac{m\pm\sqrt{m^2-216}}{6}$.

$x=2$

$\dfrac{m\pm\sqrt{m^2-216}}{6}=2$

$m\pm\sqrt{m^2-216}=12$

$\pm\sqrt{m^2-216}=12-m$

$(\pm\sqrt{m^2-216})^2=(12-m)^2$

$m^2-216=144-24m+m^2$

$24m=216+144~~\Rightarrow~~24m=360~~\Rightarrow~~m=\dfrac{360}{24}$

$\boxed{m=15}$