Question

Resolva as seguintes equaçoes do 2° grau
a) 6x ao quadrado + x - 1= 0
b) 3x ao quadrado - 7x + 2 = 0
c) 2x ao quadrado - 7x = 15
d) 4x ao quadrado + 9 = 12x

Answer 1

a)  6x²+x-1=0
a=6
b=1
c=-1
Δ=b²-4ac
Δ= 1+24=25
√Δ=5

$x'= \frac{-1+5}{12} = \frac{4}{12} = \frac{1}{3}$

$x"= \frac{-1-5}{12} = \frac{-6}{12} = \frac{-1}{2}$

$S= {{ \frac{-1}{2} , \frac{1}{3} }$}


b)  3x²-7x+2=0
a=3
b=-7
c=2

Δ=49-24=25
√Δ=5

$x'= \frac{7+5}{6} = \frac{12}{6} =2$

$x"= \frac{7-5}{6} = \frac{2}{6} = \frac{1}{3}$

$S={ { \frac{1}{3}, \frac{2}{} }$}

c)  2x²-7x-15=0
a=2
b=-7
c=-15

Δ=49+120=169
√Δ=13

$x'= \frac{7+13}{4} = \frac{20}{4} =5$

$x"= \frac{7-13}{4} = \frac{-6}{4} = \frac{-3}{2}$

$S= { { \frac{-3}{2} , \frac{5}{} }$ }

d)

4x²-12x+9=0
a=4
b=-12
c=9

Δ=144-144=0

$x'=x"= \frac{12}{8} = \frac{3}{2}$

$S={ { \frac{3}{2} }$}