Question

1 –Determine as raízes das equações A) x² + 3x - 18 = 0 e B) - 3 x² + 10 x - 3 = 0,

Answer 1

Explicação passo-a-passo:

a) $\sf x^2+3x-18=0$

$\sf \Delta=3^2-4\cdot1\cdot(-18)$

$\sf \Delta=9+72$

$\sf \Delta=81$

$\sf x=\dfrac{-3\pm\sqrt{81}}{2\cdot1}=\dfrac{-3\pm9}{2}$

$\sf x'=\dfrac{-3+9}{2}~\longrightarrow~x'=\dfrac{6}{2}~\longrightarrow~x'=3$

$\sf x"=\dfrac{-3-9}{2}~\longrightarrow~x"=\dfrac{-12}{2}~\longrightarrow~x"=-6$

As raízes são $\sf -6$ e $\sf 3$

b) $\sf -3x^2+10x-3=0$

$\sf \Delta=10^2-4\cdot(-3)\cdot(-3)$

$\sf \Delta=100-36$

$\sf \Delta=64$

$\sf x=\dfrac{-10\pm\sqrt{64}}{2\cdot(-3)}=\dfrac{-10\pm8}{-6}$

$\sf x'=\dfrac{-10+8}{-6}~\longrightarrow~x'=\dfrac{-2}{-6}~\longrightarrow~x'=\dfrac{1}{3}$

$\sf x"=\dfrac{-10-8}{-6}~\longrightarrow~x"=\dfrac{-18}{-6}~\longrightarrow~x"=3$

As raízes são $\sf \dfrac{1}{3}$ e $\sf 3$