Question

5-Achar as raizes das equaçoes
a)x²-x-20=0
b)x²-3x-4=0
c)x²-8x+7=0

Answer 1

$a)~x^{2}-x-20=0 \\ \\ \Delta~=b^{2}-4.a.c \\ \Delta~=(-1)^{2}-4.1.(-20) \\ \Delta~=1+80 \\ \Delta~=81 \\ \\ x= \frac{-b\pm\sqrt{\Delta~}}{2a} \\ x=\frac{1\pm \sqrt{81}}{2.1} \\ x= \frac{1\pm9}{2} \\ \\ x'= \frac{1+9}{2}=5 \\ x''= \frac{1-9}{2}=-4$

$b)~x^{2}-3x-4=0 \\ \\ \Delta~=b^{2}-4.a.c \\ \Delta~= (-3)^{2}-4.1.(-4) \\ \Delta~=9+16 \\ \Delta~=25 \\ \\ x= \frac{-b\pm \sqrt{\Delta~}}{2a} \\ x= \frac{3\pm \sqrt{25}}{2.1} \\ x= \frac{3\pm5}{2} \\ \\ x'= \frac{3+5}{2}=4 \\ x''= \frac{3-5}{2}=-1$

$c)~x^{2}-8x+7=0 \\ \\ \Delta~=b^{2}-4.a.c \\ \Delta~=(-8)^{2}-4.1.7 \\ \Delta~=64-28 \\ \Delta~=36 \\ \\ x= \frac{-b\pm \sqrt{\Delta~}}{2a} \\ x= \frac{8\pm \sqrt{36}}{2.1} \\ x= \frac{8\pm6}{2} \\ \\ x'= \frac{8+6}{2}=7 \\ x''= \frac{8-6}{2}=1$