Question

alguem pode me ajudar a resolver essa questão?

-2x²+9x18=0

Answer 1

Observe que:

 

$\text{x}=\dfrac{-\text{b}\pm\sqrt{\text{b}^2-4\cdot\text{a}\cdot\text{c}}}{2\cdot\text{a}}$

 

Na equação $-2\text{x}^2+9\text{x}+18=0$, temos, $\text{a}=-2, \text{b}=9$ e $\text{c}=18$, logo:

 

$\text{x}=\dfrac{-9\pm\sqrt{9^2-4\cdot(-2)\cdot18}}{2\cdot(-2)}}=\dfrac{-9\pm15}{-4}$

 

Logo, as raízes são:

 

$\text{x}'=\dfrac{-9+15}{-4}=\dfrac{-6}{-4}=\dfrac{3}{2}$

 

$\text{x}"=\dfrac{-9-15}{-4}=\dfrac{-24}{-4}=6$

 

$\text{S}=\{\frac{3}{2},6\}$