Question

4- Determine as raízes das equações abaixo, sendo U = R:
a) 6x² - 384 = 0
b) -2x² + 16x – 30 = 0

Answer 1

a) $6x^2-384=0$

$6x^2=384$

$x^2=\frac{384}{6}$

$x^2=64$

$x=$ ± $\sqrt{64}$

$x=$ ± $8$

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

b) $-2x^2+16x-30=0$

$\frac{-2x^2+16x-30}{-2}=\frac{0}{-2}$

$x^2-8x+15=0$

$\triangle=b^2-4.a.c=(-8)^2-4.1.15=64-60=4$

$x_1=\frac{-b+\sqrt{\triangle} }{2a}=\frac{8+\sqrt{4} }{2.1}=\frac{8+2}{2}=\frac{10}{2}=5$

$x_2=\frac{-b-\sqrt{\triangle} }{2a}=\frac{8-\sqrt{4} }{2.1}=\frac{8-2}{2}=\frac{6}{2}=3$

$S=\{3,\ 5\}$