Question

Resolva as equações do segundo grau e dê seu conjunto solução.

a) x²-2x-8=0
b) x²-3x+4=6-2x

Answer 1

$a) x^{2} -2x-8=0\\\\\\ a=1;b=-2;c=-8\\\\ \Delta=b^2-4ac\to \Delta=(-2)^2-4*1*(-8)\to \Delta=4+32\to \Delta=36\\\\ x= \frac{-b+- \sqrt{\Delta} }{2a} \to x= \frac{-(-2)+- \sqrt{36} }{2*1} \to x= \frac{2+- 6 }{2} \to \\\\ x'= \frac{2+ 6 }{2} \to x'= \frac{8 }{2} \to x'=4\\\\ x''= \frac{2- 6 }{2} \to x''= \frac{-4 }{2} \to x''=-2\\\\\\ S=(-2;4)$








$b) x^{2} -3x+4=6-2x\\\\\\ x^{2} -3x+4-6+2x=0\to\\\\ x^{2} -x-2=0\\\\ a=1;b=-1;c=-2\\\\ \Delta=b^2-4ac\to \Delta=(-1)^2-4*1*(-2)\to \Delta=1+8\to \Delta=9\\\\ x= \frac{-b+- \sqrt{\Delta} }{2a} \to x= \frac{-(-1)+- \sqrt{9} }{2*1} \to x= \frac{1+- 9 }{2} \to \\\\ x'= \frac{1+9 }{2} \to x'= \frac{10 }{2} \to x'=5\\\\ x''= \frac{1- 9 }{2} \to x''= \frac{-8 }{2} \to x''=-4\\\\\\ S=(-4;5)$



Espero ter ajudado...