Question

x2 - 3x – 4 = 0
b) x2 - 8x + 12 = 0
c) x2 + 6x + 5 = 0
d) 4x2 9 = 12x
e) 2x2 +12x + 18 = 0
f) x2 - 2x – 2 = 0

URGENTE

Answer 1

Explicação passo-a-passo:

a) x² -3x -4

 (x -4)×(x+1)

x'= 4   x"= -1

b) x² -8x +12

 (x -6)×(x -2)

x'= 6   x"= 2

c) x² +6x +5

  (x +5)×(x+1)

x'= -5   x"= -1

d) 4x² +9 = 12x

   4x² -12x +9

Δ= (-12)² -4×4×9    $x= \frac{12+-6\sqrt{2} }{2.4}$

Δ= 144 -72            $x'= \frac{12 +6\sqrt{2} }{8} = \frac{6 +3 \sqrt{2} }{4}$

Δ= 72                    $x"= \frac{12-6\sqrt{2} }{8}=\frac{6-3\sqrt{2} }{4}$

e) 2x² +12x +18  simplifique (facilita)

   x² +6x +9

(x +3)×(x +3)

x= -3

f) x² -2x – 2

Δ= (-2)² -4×1×(-2)    $x=\frac{2+-2\sqrt{3} }{2}$

Δ= 4 +8                 $x'= \frac{2 +2\sqrt{3} }{2} = 1 +\sqrt{3}$

Δ= 12                     $x"= \frac{2 -2\sqrt{3} }{2} = 1 -\sqrt{3}$