Question

1- Calcule a soma e o produto das raízes das equações, sem resolvê-las,
a) x2 – 5x + 6 = 0
d) 2x2 – 10x - 12 = 0
b) 3x2 - 21x + 9 = 0
e) x2 – 2x – 8 = 0
c) 3x2 + 10x + 3 = 0
f) 9x2 - 12x – 1= 0​

Answer 1

Resposta:

a) R: x1= 3, x2= 2

d) R: x1= 6, x2= -1

b) R: não consegui terminar

e) R: x1= -4, x2= -2

c) R: x1= -1/3, x2=-3

f) R: x1= 2+ raiz 5/3, x2= 2- raiz 5/3

Explicação passo-a-passo:

◇ (delta)

a) x2-5x+6=0 5+-1/2=

◇= (-5^2)-4×1×6 5+1/2= x1= 3

◇= 25-24 5-1/2= x2= 2

◇=1

d) 2x2-10x-12=0 10+-14/4=

◇= (-10^2)-4×2×(-12) 10+14/4= x1= 6

◇= 100+96 10-14/4= x2= -1

◇= 196

b) 3x2-21x+9=0

◇= (-21^2)-4×3×9

◇= 441-4×27

◇= 441-108

◇= 333

e) x2-2x-8=0 2+-6/2=

◇= (-2^2)-4×1×(-8) 2+6/2= x1=4

◇= 4+32 2-6/2= x2= -2

◇= 36

c) 3x2+10x+3=0 -10+-8/6=

◇= (-10^2)-4×3×3 -10+8/6= x1= -1/3

◇= 100-4×9 -10-8/6= x2= -3

◇= 100-36

◇= 64

f) 9x2-12x-1=0 12+-6 raiz 5/18=

◇= -12^2-4×9×(-1) x1= 2+ raiz 5/3

◇= 144+36 x2= 2-raiz 5/3

◇= 180