Question

resolva as equações de 2' grau com cálculo

X^2-5X+6=0

X^2-8X+12=0

X^2-6X+9=0

X^2+5X7=0

Answer 1

$A) x^2-5x+6=0\\\\\Delta=(-5)^2-4\cdot(1)\cdot(6)\\\Delta=25-24\\\Delta=1\\\\x=\frac{-(-5)\pm\sqrt1}{2\cdot1}\to x=\frac{5\pm1}{2}\\\\x'=\frac{5+1}{2}=3\\\\x''=\frac{5-1}{2}=2\\\\s=\{2,3\}\\\\\\B) x^2-8x+12=0\\\\\Delta=(-8)^2-4\cdot(1)\cdot(12)\\\Delta=64-48\\\Delta=16\\\\x=\frac{-(-8)\pm\sqrt16}{2\cdot1}\to x=\frac{8\pm4}{2}\\\\x'=\frac{8+4}{2}=6\\\\x''=\frac{8-4}{2}=2\\\\s=\{2,6\}$


$C) x^2-6x+9=0\\\\\Delta=(-6)^2-4\cdot(1)\cdot(9)\\\Delta=36-36\\\Delta=0\\\\x=\frac{-(-6)\pm\sqrt0}{2\cdot1}\\\\x'=\frac{6}{2}=3\\\\s=\{3\} \\\\\\D) x^2+5x+7=0\\\\\Delta=(5)^2-4\cdot(1)\cdot(7)\\\Delta=25-28\\\Delta=-3\\\\s=\{\}$

Obs: Considerando as soluções apenas em R.