Question

Resolva as equações do segundo grau. a) x² + 3x-28=0 b) 2x² - 50 = 0 c) x² - 12x + 36 = 0 d) 4x² - 20x = 0 e) - x² + x + 12 = 0 f) x² - 6x + 9 = 0 g) x² + 6x + 9 =0 h) 7x² + x + 1 = 0 i) x² - 13x + 12 = 0 j) x² + 13x + 40 = 0​

Answer 1

Equação do segundo grau

Explicação passo a passo:

a) x² + 3x-28=0

$\frac{-3\pm \sqrt{3^2-4\cdot \:1\cdot \left(-28\right)}}{2\cdot \:1}$

             $x_1=\frac{-3+11}{2\cdot \:1}=4$

$\frac{-3\pm \:11}{2\cdot \:1}$  

             $x_2=\frac{-3-11}{2\cdot \:1}=-7$

b) 2x² - 50 = 0

  $2x^2=50\\x^{2} =\frac{50}{2}\\x^2=25\\x=\pm \sqrt{25}\\x=\pm 5\\S:[5,-5]$

c) x² - 12x + 36 = 0

  $\frac{-\left(-12\right)\pm \sqrt{\left(-12\right)^2-4\cdot \:1\cdot \:36}}{2\cdot \:1}$

$\frac{-\left(-12\right)\pm \sqrt{0}}{2\cdot \:1}$

$\frac{-\left(-12\right)}{2\cdot \:1}=6$

d) 4x² - 20x = 0

$\frac{-\left(-20\right)\pm \sqrt{\left(-20\right)^2-4\cdot \:4\cdot \:0}}{2\cdot \:4}$

                    $x_1=\frac{-\left(-20\right)+20}{2\cdot \:4}=5$

$\frac{-\left(-20\right)\pm \:20}{2\cdot \:4}$

                   $x_2=\frac{-\left(-20\right)-20}{2\cdot \:4}=0$

e) - x² + x + 12 = 0

$\frac{-1\pm \sqrt{1^2-4\left(-1\right)\cdot \:12}}{2\left(-1\right)}$

        $x_1=\frac{-1+7}{2\left(-1\right)}=-3$

$\frac{-1\pm \:7}{2\left(-1\right)}$

         $\:x_2=\frac{-1-7}{2\left(-1\right)}=4$

f) x² - 6x + 9 = 0

$\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:1\cdot \:9}}{2\cdot \:1}$

$\frac{-\left(-6\right)\pm \sqrt{0}}{2\cdot \:1}$

$x=\frac{-\left(-6\right)}{2\cdot \:1}=3$

g) x² + 6x + 9 =0

$\frac{-6\pm \sqrt{6^2-4\cdot \:1\cdot \:9}}{2\cdot \:1}$

$\frac{-6\pm \sqrt{0}}{2\cdot \:1}$

$x=\frac{-6}{2\cdot \:1}=-3$

X h) 7x² + x + 1 = 0 X    <----Sem resultados a essa questão digite corretamente na proxima

i) x² - 13x + 12 = 0

$\frac{-\left(-13\right)\pm \sqrt{\left(-13\right)^2-4\cdot \:1\cdot \:12}}{2\cdot \:1}$

              $x_1=\frac{-\left(-13\right)+11}{2\cdot \:1}=12$

$\frac{-\left(-13\right)\pm \:11}{2\cdot \:1}$

             $x_2=\frac{-\left(-13\right)-11}{2\cdot \:1}=1$

j) x² + 13x + 40 = 0​

$\frac{-13\pm \sqrt{13^2-4\cdot \:1\cdot \:40}}{2\cdot \:1}$

           $x_1=\frac{-13+3}{2\cdot \:1}=-5$

$\frac{-13\pm \:3}{2\cdot \:1}$

            $x_2=\frac{-13-3}{2\cdot \:1}=-8$