Question

Pela fórmula de Bhaskara , dê o conjunto solução das equações do 2°grau abaixo.

A)
{x}^{2} + 2x - 48 = 0
B)
2 {x}^{2} - 7x + 3 = 0

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Answer 1

Explicação passo-a-passo:

a) $\sf x^2+2x-48=0$

$\sf \Delta=2^2-4\cdot1\cdot(-48)$

$\sf \Delta=4+192$

$\sf \Delta=196$

$\sf x=\dfrac{-2\pm\sqrt{196}}{2\cdot1}=\dfrac{-2\pm14}{2}$

$\sf x'=\dfrac{-2+14}{2}~\longrightarrow~x'=\dfrac{12}{2}~\longrightarrow~x'=6$

$\sf x"=\dfrac{-2-14}{2}~\longrightarrow~x"=\dfrac{-16}{2}~\longrightarrow~x'=-8$

$\sf S=\{-8,6\}$

b) $\sf 2x^2-7x+3=0$

$\sf \Delta=(-7)^2-4\cdot2\cdot3$

$\sf \Delta=49-24$

$\sf \Delta=25$

$\sf x=\dfrac{-(-7)\pm\sqrt{25}}{2\cdot2}=\dfrac{7\pm5}{4}$

$\sf x'=\dfrac{7+5}{4}~\longrightarrow~x'=\dfrac{12}{4}~\longrightarrow~x'=3$

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

$\sf S=\left\{\dfrac{1}{2},3\right\}$

Answer 2

A)S=(6;-8)

B)S=(3;0,5)