Question

responda agora qual o formato do gráfico de acordo com as figuras acima: para aonde está abertura, se toca o eixo x em 1 ou 2 lugares e se tem a soluçao real.
a) x² - 5x + 6=0 b) x² - 8x + 12=0 c) + 2x - 8 =0 d)x² - 4x - 5=0 e) -x² + x + 12=0 f) -x² + 6x - 5=0

Answer 1

Resposta:

a) a=1  b=-5  c=6

$X=\frac{-(-5)+/-\sqrt{((-5)^{2}-4.1.6 } }{1.2}$

$X=\frac{+5+/-\sqrt{25-24} }{2}$

$X=\frac{+5+/-\sqrt{1} }{2}$

$X=\frac{+5+/-1}{2}$

$X1=\frac{+5-1}{2}=\frac{4}{2}=2\\X2=\frac{+5+1}{2}=\frac{6}{2}=3$           S{2,3}

b) a=1  b=-8  c=+12

$X=\frac{-(-8)+/-\sqrt{(-8)^{2}-4.1.+12 } }{1.2}\\X=\frac{+8+/-\sqrt{64-48} }{2}\\X=\frac{+8+/-\sqrt{16} }{2}\\X=\frac{+8+/-4}{2}\\X1=\frac{+8-4}{2}=\frac{4}{2}=2\\X2=\frac{+8+4}{2}=\frac{12}{2}=6$S{2,6}

c) a=2  b=0  c=8

$X=\frac{-0+/-\sqrt{0^{2}-4.2.8 } }{2.2}\\X=\frac{-0+/-\sqrt{0-64} }{4}\\X=\frac{-0+/-64}{4}\\X1=\frac{-64}{4}=-16\\X2=\frac{+64}{4}=+16$        S{-16,+16}

d) a=1  b=-4  c=-5

$X=\frac{-(-4)+/-\sqrt{(-4)^{2}-4.1.-5 } }{2.1}\\X=\frac{+4+/-\sqrt{16+20} }{2}\\X=\frac{4+/-\sqrt{36} }{2}$Não tem solução

e) a=-1  b=1  c=12

$X=\frac{-1+/-\sqrt{1^{2}-4.-1.12 } }{-1.2}\\X=\frac{-1+/-\sqrt{1+48} }{-2}\\X=\frac{-1+/-\sqrt{49} }{-2}\\X=\frac{-1+/-7}{-2}\\X1=\frac{-1-7}{-2}=\frac{-8}{-2}=+4\\X2=\frac{-1+7}{-2}=\frac{+6}{-2}=-3$     S{4,-3}

f) a=-1  b=+6  c=-5

$X=\frac{-6+/-\sqrt{6^{2}-4.-1.-5 } }{-1.2}\\X=\frac{-6\sqrt{36-20} }{-2} \\X=\frac{-6+/-\sqrt{4} }{-2}\\X=\frac{-6+/-2}{-2}\\X1=\frac{-6-2}{-2}=\frac{-8}{-2}=+4\\X2=\frac{-6+2}{-2}=\frac{-4}{-2}=+2$    S{4,2}