Question

7.determine os valores de X para as inequações do segundo grau :

e)x²+4x-12≥0
f)2x²+10x+12≥0
g)4x²+24x+20<0

Answer 1

E)

x²+4x-12≥0

transformamos numa equação do 2°

x²+4x-12=0

aplicamos a formula de baskhara

$\Delta= B^{2}-4.A.C$

$\Delta= 4^{2}-4.1.(-12)\\\Delta= 16+48\\\Delta=64$

$\frac{-B \pm\sqrt{\Delta}}{2.A}$

$\frac{-4 \pm\sqrt{8}}{2.1}\\\\\frac{-4 \pm8}{2}\\\\\frac{4}{2}=2\\\\\frac{-12}{2}= (-6)$

S= 6 ≥ x ≤ 2

F)

2x²+10x+12≥0

transformando em 2°

2x²+10x+12=0

aplicando a formula

$\Delta= 10^{2}-4.2.12\\\Delta= 100-96\\\Delta=4$

$\frac{-10\pm\sqrt{4}}{2.2}\\\\\frac{-10 \pm2}{4}\\\\\frac{-8}{4}=-2\\\\\frac{-12}{4}= (-3)$

solução

S= -3≤x≥ -2

G)

4x²+24x+20<0

Transformando numa de 2°

4x²+24x+20=0

$\Delta= 24-4.4.20\\\Delta= 676-320\\\Delta=256\\\Delta=16$

$\frac{-24\pm\sqrt{256}}{2.4}\\\\\frac{-24 \pm16}{8}\\\\\frac{-8}{8}=-1\\\\\frac{-40}{8}= (-5)$

S=$-5<x<-1\:$