Question

SOCORRO!!!

5)As raízes da equação x2 + 5x/2 - 3/2 = 0 são:
O 2 e 5
-2 e 1/3
O
-3 e 1/2
4 e 1/5​

Answer 1

Explicação passo-a-passo:

$x^2+\dfrac{5x}{2}-\dfrac{3}{2}=0$

$2x^2+5x-3=0$

$\Delta=5^2-4\cdot2\cdot(-3)$

$\Delta=25+24$

$\Delta=49$

$x=\dfrac{-5\pm\sqrt{49}}{2\cdot2}=\dfrac{-5\pm7}{4}$

$x'=\dfrac{-5+7}{4}~\longrightarrow~x'=\dfrac{2}{4}~\longrightarrow~x'=\dfrac{1}{2}$

$x"=\dfrac{-5-7}{4}~\longrightarrow~x"=\dfrac{-12}{4}~\longrightarrow~x"=-3$

As raízes são $-3$ e $\dfrac{1}{2}$

Answer 2

Oie, Td Bom?!

$x {}^{2} + \frac{5x}{2} - \frac{3}{ 2} = 0 \\ 2x {}^{2} + 5x - 3 = 0 \\ 2x {}^{2} + 6x - x - 3 = 0 \\ 2x \: . \: (x + 3) - (x + 3) = 0 \\ (x + 3) \: . \: (2x - 1) = 0$

$x + 3 = 0⟶x = - 3 \\ 2x - 1 =0⟶x = \frac{1}{2}$

S = $\left \{ x_{1} = - 3 \: , \: x_{2} = \frac{1}{2} \right \}$

Att. Makaveli1996