Question

SÓ ESSA QUESTÃO EU PRECISO DE AJUDA
Resolva e apresente o conjunto solução das seguintes equações de segunda grau:
a) 1x² - x - 20 = 0
b) 1x² - 3x - 4 = 0
c) x² - 8x + 7 = 0
d) 3x² - 147 = 0
e) 2x² + 20x = 0​

Answer 1

Resposta:

Explicação passo a passo:

$a)$

$x^{2} -x-20=0$

$a=1\\b=-1\\c=-20$

$\Delta=b^{2} -4ac$

$\Delta=(-1)^{2} -4.(1).(-20)$

$\Delta=1+80$

$\Delta=81$

$x=\frac{-b\pm\sqrt{\Delta} }{2a}$

$x=\frac{-(-1)\pm\sqrt{81} }{2.(1)}$

$x=\frac{1\pm9 }{2}$

$x'=\frac{1+9}{2} =>x'=\frac{10}{2}=>x'=5$

$x''=\frac{1-9}{2} =>x'=-\frac{8}{2}=>x''=-4$

$S=\{-4;5\}$

$b)$

$x^{2} -3x-4=0$

$a=1\\b=-3\\c=-4$

$\Delta=b^{2} -4ac$

$\Delta=(-3)^{2} -4.(1).(-4)$

$\Delta=9+16$

$\Delta=25$

$x=\frac{-b\pm\sqrt{\Delta} }{2a}$

$x=\frac{-(-3)\pm\sqrt{25} }{2.(1)}$

$x=\frac{3\pm5}{2}$

$x'=\frac{3+5}{2} =>x'=\frac{8}{2}=>x'=4$

$x''=\frac{3-5}{2} =>x'=-\frac{2}{2}=>x''=-1$

$S=\{-1;4\}$

$c)$

$x^{2} -8x+7=0$

$a=1\\b=-8\\c=7$

$\Delta=b^{2} -4ac$

$\Delta=(-8)^{2} -4.(1).(7)$

$\Delta=64-28$

$\Delta=36$

$x=\frac{-b\pm\sqrt{\Delta} }{2a}$

$x=\frac{-(-8)\pm\sqrt{36} }{2.(1)}$

$x=\frac{8\pm6 }{2}$

$x'=\frac{8+6}{2} =>x'=\frac{14}{2}=>x'=7$

$x''=\frac{8-6}{2} =>x'=\frac{2}{2}=>x''=1$

$S=\{1;7\}$

$d)$

$3x^{2} -147=0$

$3x^{2} =147$

$x^{2} =147/3$

$x^{2} =49$

$x=\pm\sqrt{49}$

$x=\pm7$

$S=\{-7;7\}$

$e)$

$2x^{2} +20x=0$

$x.(2x+20)=0$

$x=0$

$ou...$

$2x+20=0$

$2x=-20$

$x=-\frac{20}{2}$

$x=-10$

$S=\{0;-10\}$