Question

Quais são os resultados?

01-3X2 -X -2 = 0

02 – 5X2 +8X +10 = 0

03 – 4X2 +8X +6 = 0

04 – X2 -4X -5 = 0

05 – 4X2 -33X +8 = 0

Answer 1

01-3 X 2 -X -2 = -1\7

$1-3X\cdot \:2-X-2=0\quad :\quad X=-\frac{1}{7}\quad \left(\mathrm{Decimal}:\quad X=-0.1428571428\dots \right)\\\\\\1-3X\cdot \:2-X-2=0\\\\1-6X-X-2=0\\\\1-7X-2=0\\\\-7X+1-2=0\\\\-7X-1=0\\\\-7X-1+1=0+1\\\\-7X=1\\\\\frac{-7X}{-7}=\frac{1}{-7}\\\\\\X=-\frac{1}{7}$

02 – 5 X 2 +8 X +10 = 0

$2-5X\cdot \:2+8X+10=0\quad :\quad X=6\\2-5X\cdot \:2+8X+10=0\\\\\\2-10X+8X+10=0\\\\2-2X+10=0\\\\-2X+2+10=0\\\\-2X+12=0\\\\-2X+12-12=0-12\\\\-2X=-12\\\\\frac{-2X}{-2}=\frac{-12}{-2}\\\\X=6$

03 – 4X2 +8X +6 = 0

$3-4X\cdot \:2+8X+6=0\quad :\quad \mathrm{Sem\:solucao}\\\\3-4X\cdot \:2+8X+6=0\\\\3-8X+8X+6=0\\\\3+6=0\\\\9=0\\\\\mathrm{Os\:lados\:nao\:sao\:iguais}$

04 – X 2 -4 X -5 = 0

$4-X\cdot \:2-4X-5=0\quad :\quad X=-\frac{1}{6}\quad \left(\mathrm{Decimal}:\quad X=-0.1666666666\dots \right)\\\\4-X\cdot \:2-4X-5=0\\\\4-6X-5=0\\\\-6X+4-5=0\\\\-6X-1=0\\\\-6X-1+1=0+1\\\\-6X=1\\\\\frac{-6X}{-6}=\frac{1}{-6}\\\\\\x=-\frac{1}{6}$

05 – 4 X 2 -3 3 X +8 = 0

$5-4X\cdot \:2-33X+8=0\quad :\quad X=\frac{13}{41}\quad \left(\mathrm{Decimal}:\quad X=0.3170731707\dots \right)\\\\\\5-4X\cdot \:2-33X+8=0\\\\\\5-41X+8=0\\\\-41X+5+8=0\\\\-41X+13=0\\\\-41X+13-13=0-13\\\\\\-41X=-13\\\\\frac{-41X}{-41}=\frac{-13}{-41}\\\\x=\frac{13}{41}$