Question

1) Aplicando a fórmula de Bhaskara, resolva as seguintes equações do 2a grau encontrando o discriminante e as raízes, se existirem da função.
a) x2 - 14x + 48=0
c) x2 + 5x – 6=0
e) x2 - 25=0
b) 3x2 +12x – 63=0
d) x2 -9x =0
f) 2x2 - 242=0
g) 4x2 - 4x – 35=0
i) 9x2 - 18x – 7=0
k) -5x2 + 12x – 14=0
m) x2 + x – 20=0
o) 4x2 - 20x + 25=0
q) –x2 + 9x – 20=0
s) -2x2 + 4x=0
u) –x2 + 4=0
h) 2x2 - x – 1=0
j) x2 + 5x -6=0
l) 4x2 + 4x -3=0
n) 5x2 - 2x + 1=0
p) x2 + 3x – 28=0
r) –x2 + 4x – 2=0
t) x2 - x -2=0

Me ajudem pf está tudo Misturado as letras pq eu só copiei oq a sora mandou tava um do lado do outro por isso ficou assim :/

Answer 1

Explicação passo-a-passo:

a) $x^2-14x+48=0$

$\Delta=b^2-4\cdot a\cdot c$

$\Delta=(-14)^2-4\cdot1\cdot48$

$\Delta=196-192$

$\Delta=4$

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

$x=\dfrac{-(-14)\pm\sqrt{4}}{2\cdot1}$

$x=\dfrac{14\pm2}{2}$

$x'=\dfrac{14+2}{2}~\longrightarrow~x'=\dfrac{16}{2}~\longrightarrow~x'=8$

$x"=\dfrac{14-2}{2}~\longrightarrow~x"=\dfrac{12}{2}~\longrightarrow~x"=6$

$S=\{6,8\}$

b) $3x^2+12x-63=0$

$\Delta=b^2-4\cdot a\cdot c$

$\Delta=12^2-4\cdot3\cdot(-63)$

$\Delta=144+756$

$\Delta=900$

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

$x=\dfrac{-12\pm\sqrt{900}}{2\cdot3}$

$x=\dfrac{-12\pm30}{6}$

$x'=\dfrac{-12+30}{2}~\longrightarrow~x'=\dfrac{18}{6}~\longrightarrow~x'=3$

$x"=\dfrac{-12-30}{6}~\longrightarrow~x"=\dfrac{-42}{6}~\longrightarrow~x"=-7$

$S=\{-7,3\}$

c) $x^2+5x-6=0$

$\Delta=b^2-4\cdot a\cdot c$

$\Delta=5^2-4\cdot1\cdot(-6)$

$\Delta=25-24$

$\Delta=1$

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

$x=\dfrac{-5\pm\sqrt{1}}{2\cdot1}$

$x=\dfrac{-5\pm1}{2}$

$x'=\dfrac{-5+1}{2}~\longrightarrow~x'=\dfrac{-4}{2}~\longrightarrow~x'=-2$

$x"=\dfrac{-5-1}{2}~\longrightarrow~x"=\dfrac{-6}{2}~\longrightarrow~x"=-3$

$S=\{-3,-2\}$

d) $x^2-9x=0$

$\Delta=b^2-4\cdot a\cdot c$

$\Delta=(-9)^2-4\cdot1\cdot0$

$\Delta=81-0$

$\Delta=81$

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

$x=\dfrac{-(-9)\pm\sqrt{81}}{2\cdot1}$

$x=\dfrac{9\pm9}{2}$

$x'=\dfrac{9+9}{2}~\longrightarrow~x'=\dfrac{18}{2}~\longrightarrow~x'=9$

$x"=\dfrac{9-9}{2}~\longrightarrow~x"=\dfrac{0}{2}~\longrightarrow~x"=0$

$S=\{0,9\}$

e) $x^2-25=0$

$\Delta=b^2-4\cdot a\cdot c$

$\Delta=0^2-4\cdot1\cdot(-25)$

$\Delta=0+100$

$\Delta=100$

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

$x=\dfrac{-0\pm\sqrt{100}}{2\cdot1}$

$x=\dfrac{0\pm10}{2}$

$x'=\dfrac{0+10}{2}~\longrightarrow~x'=\dfrac{10}{2}~\longrightarrow~x'=5$

$x"=\dfrac{0-10}{2}~\longrightarrow~x"=\dfrac{-10}{2}~\longrightarrow~x"=-5$

$S=\{-5,5\}$

f) $2x^2-242=0$

$\Delta=b^2-4\cdot a\cdot c$

$\Delta=0^2-4\cdot2\cdot(-242)$

$\Delta=0+1936$

$\Delta=1936$

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

$x=\dfrac{-0\pm\sqrt{1936}}{2\cdot2}$

$x=\dfrac{0\pm44}{4}$

$x'=\dfrac{0+44}{4}~\longrightarrow~x'=\dfrac{44}{4}~\longrightarrow~x'=11$

$x"=\dfrac{0-44}{4}~\longrightarrow~x"=\dfrac{-44}{4}~\longrightarrow~x"=-11$

$S=\{-11,11\}$

g) $4x^2-4x-35=0$

$\Delta=b^2-4\cdot a\cdot c$

$\Delta=(-4)^2-4\cdot4\cdot(-35)$

$\Delta=16+560$

$\Delta=576$

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

$x=\dfrac{-(-4)\pm\sqrt{576}}{2\cdot4}$

$x=\dfrac{4\pm24}{8}$

$x'=\dfrac{4+24}{8}~\longrightarrow~x'=\dfrac{28}{8}~\longrightarrow~x'=\dfrac{7}{2}$

$x"=\dfrac{4-24}{8}~\longrightarrow~x"=\dfrac{-20}{8}~\longrightarrow~x"=\dfrac{-5}{2}$

$S=\left\{\dfrac{-5}{2},\dfrac{7}{2}\right\}$

h) $2x^2-x-1=0$

$\Delta=b^2-4\cdot a\cdot c$

$\Delta=(-1)^2-4\cdot2\cdot(-1)$

$\Delta=1+8$

$\Delta=9$

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

$x=\dfrac{-(-1)\pm\sqrt{9}}{2\cdot2}$

$x=\dfrac{1\pm3}{4}$

$x'=\dfrac{1+3}{2}~\longrightarrow~x'=\dfrac{4}{4}~\longrightarrow~x'=1$

$x"=\dfrac{1-3}{4}~\longrightarrow~x"=\dfrac{-2}{4}~\longrightarrow~x"=\dfrac{-1}{2}$

$S=\left\{\dfrac{-1}{2},1\right\}$

i) $9x^2-18x-7=0$

$\Delta=b^2-4\cdot a\cdot c$

$\Delta=(-18)^2-4\cdot9\cdot(-7)$

$\Delta=324+252$

$\Delta=576$

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

$x=\dfrac{-(-18)\pm\sqrt{576}}{2\cdot9}$

$x=\dfrac{18\pm24}{18}$

$x'=\dfrac{18+24}{18}~\longrightarrow~x'=\dfrac{42}{18}~\longrightarrow~x'=\dfrac{7}{3}$

$x"=\dfrac{18-24}{18}~\longrightarrow~x"=\dfrac{-6}{18}~\longrightarrow~x"=\dfrac{-1}{3}$

$S=\left\{\dfrac{-1}{3},\dfrac{7}{3}\right\}$

j) $x^2+5x-6=0$

$\Delta=b^2-4\cdot a\cdot c$

$\Delta=5^2-4\cdot1\cdot(-6)$

$\Delta=25-24$

$\Delta=1$

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

$x=\dfrac{-5\pm\sqrt{1}}{2\cdot1}$

$x=\dfrac{-5\pm1}{2}$

$x'=\dfrac{-5+1}{2}~\longrightarrow~x'=\dfrac{-4}{2}~\longrightarrow~x'=-2$

$x"=\dfrac{-5-1}{2}~\longrightarrow~x"=\dfrac{-6}{2}~\longrightarrow~x"=-3$

$S=\{-3,-2\}$

k) $-5x^2+12x-14=0$

$\Delta=b^2-4\cdot a\cdot c$

$\Delta=12^2-4\cdot(-5)\cdot(-14)$

$\Delta=144-280$

$\Delta=-136$

Não há raízes reais

$S=\{~\}$