Question

1-Resolva as raízes complexas usando a fórmula de bhaskara .

• 2X²+8X+10

• X²+3X+9=0

Answer 1

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

==

$2x^2 + 8x +10 = 0$

Podemos dividir por 2 para facilitar os cálculos, não altera o resultado:

$x^2 + 4x + 5 = 0$

Δ = b²−4ac
Δ = (4)²−4⋅1⋅5
Δ = 16−20
Δ = −4

$x = \dfrac{-4 \pm \sqrt{-4}}{2*1}\\ \\ x = \dfrac{-4 \pm \sqrt{4}.i}{2}\\ \\ x' = \dfrac{-4 + 2.i}{2}\\ \\ x' = -2\\ \\ \\ x'' = \dfrac{-4 - 2.i}{2}\\ \\ x'' = -2$


S = {-2, -2}

====
$x^{2} -3x + 9 = 0$


Δ = b²−4ac
Δ = (−3)²−4⋅1⋅9
Δ = 9−36
Δ = −27

$x = \dfrac{-(-3) \pm \sqrt{-27}}{2*1}\\ \\ x = \dfrac{3 \pm \sqrt{27}.i}{2}\\ \\ x' = \dfrac{3 + \sqrt{27}.i}{2}\\ \\ x' = \dfrac{3 + 3\sqrt{3}.i}{2}\\ \\ \\x'' = \dfrac{3 - \sqrt{27}.i}{2}\\ \\ x'' = \dfrac{3 - 3\sqrt{3}.i}{2}$


S = {$\dfrac{3 + 3\sqrt{3}.i}{2}, ~\dfrac{3 - 3\sqrt{3}.i}{2}$}