Question

1) DETERMINE AS RAÍZES DAS EQUAÇÕES ABAIXO:

A)X²-2X+1=0

B)2X²+4X-6=0

C)-X²-4X+5=0

D)X²-X-20=0

E)X²-3X-4=0

F)X²-8X+7=0

ME AJUDEM POR FAVOR GENTE...​

Answer 1

Explicação passo a passo:

A)X²-2X+1=0

 $X^2-2X+1=0\\X_{1,\:2}=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:1\cdot \:1}}{2\cdot \:1}\\\\X_{1,\:2}=\frac{-\left(-2\right)\pm \sqrt{0}}{2\cdot \:1}\\\\X=\frac{-\left(-2\right)}{2\cdot \:1}\\\\X=1$

B)2X²+4X-6=0

  $2X^2+4X-6=0\\X_{1,\:2}=\frac{-4\pm \sqrt{4^2-4\cdot \:2\left(-6\right)}}{2\cdot \:2}\\\\X_{1,\:2}=\frac{-4\pm \:8}{2\cdot \:2}\\\\X_1=\frac{-4+8}{2\cdot \:2}=1,\:X_2=\frac{-4-8}{2\cdot \:2}=-3\\\\S[1,-3]$

C)-X²-4X+5=0

   $-X^2-4X+5=0\\\\X_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\left(-1\right)\cdot \:5}}{2\left(-1\right)}\\\\X_{1,\:2}=\frac{-\left(-4\right)\pm \:6}{2\left(-1\right)}\\\\X_1=\frac{-\left(-4\right)+6}{2\left(-1\right)}=-5,\:X_2=\frac{-\left(-4\right)-6}{2\left(-1\right)}=1\\\\S[-5,1]$

D)X²-X-20=0

  $X_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{\left(-1\right)^2-4\cdot \:1\cdot \left(-20\right)}}{2\cdot \:1}\\\\X_{1,\:2}=\frac{-\left(-1\right)\pm \:9}{2\cdot \:1}\\\\X_1=\frac{-\left(-1\right)+9}{2\cdot \:1}=5,\:X_2=\frac{-\left(-1\right)-9}{2\cdot \:1}=-4\\\\S[5,-4]$

E)X²-3X-4=0

 $X_{1,\:2}=\frac{-\left(-3\right)\pm \sqrt{\left(-3\right)^2-4\cdot \:1\cdot \left(-4\right)}}{2\cdot \:1}\\\\X_{1,\:2}=\frac{-\left(-3\right)\pm \:5}{2\cdot \:1}\\\\X_1=\frac{-\left(-3\right)+5}{2\cdot \:1}=4,\:X_2=\frac{-\left(-3\right)-5}{2\cdot \:1}=-1\\\\S[4,-1]$

F)X²-8X+7=0

 $X_{1,\:2}=\frac{-\left(-8\right)\pm \sqrt{\left(-8\right)^2-4\cdot \:1\cdot \:7}}{2\cdot \:1}\\\\X_{1,\:2}=\frac{-\left(-8\right)\pm \:6}{2\cdot \:1}\\\\X_1=\frac{-\left(-8\right)+6}{2\cdot \:1}=7,\:X_2=\frac{-\left(-8\right)-6}{2\cdot \:1}=1\\\\S[7,1]$