Question

Olá, preciso de uma ajudinha pra fazer algumas contas, valendo 100 pontos.
No maximo ate amanha preciso das respostas, contas completas
1) 2x²-7x-15=0
2) 4x²-12x+9=0
3) x²- x-12=0
4)2x²+12x+18=0
5)x²-4x+9=0
6)25x²-20x-4=0
7)x²-2x-15=0
8)x²+3x+2=0

Answer 1

1)
$2x^2-7x-15=0\\ \Delta=(-7)^2-4.2.(-15)=49+120=169\\ x=\frac{7\pm\sqrt{169}}{2.2}=\frac{7\pm13}{4}\\ \\ x_1=\frac{7-13}{4}=-\frac{6}{4}=-\frac{3}{2}\\ \\ x_2=\frac{7+13}{4}=\frac{20}{4}=5$

2)
$4x^2-12x+9=0\\ \Delta=(-12)^2-4.4.9=144-144=0\\ \\ x=\frac{12}{8}=\frac{3}{2}$

3)
$x^2-x-12=0\\ \Delta=(-1)^2-4.1.(-12)=1+48=49\\ \\ x=\frac{1\pm\sqrt{49}}{2}=\frac{1\pm7}{2}\\ \\ x_1=\frac{1-7}{2}=-\frac{6}{2}=-3\\ \\ x_2=\frac{1+7}{2}=\frac{8}{2}=4$


4)
$2x^2+12x+18=0\\ \Delta=12^2-4.2.18=144-144=0\\ \\ x=\frac{-12}{2.2}=-\frac{12}{4}=-3$

5)
$x^2-4x+9=0\\ \Delta=(-4)^2-4.1.9=16-36=-20\\ \\ \Delta<0 \Rightarrow nao \ existem \ raizes \ reais$

6)
$25x^2-20x-4=0\\ \Delta=(-20)^2-4.25.(-4)=400+400=800\\ \\ x=\frac{20\pm\sqrt{800}}{2.25}=\frac{20\pm20\sqrt2}{50}=\frac{2\pm2\sqrt2}{5}$

7)
$x^2-2x-15=0\\ \Delta=(-2)^2-4.1.(-15)=4+60=64\\ \\ x=\frac{2\pm\sqr{64}}{2}=\frac{2\pm8}{2}\\ \\ x_1=-3\\ \\ x_2=5$

8)
$x^2+3x+2=0\\ \Delta=3^2-4.1.2=9-8=1\\ \\ x=\frac{-3\pm\sqrt1}{2}=\frac{-3\pm1}{2}\\ \\ x_1=-2\\ \\ x_2=-1$