Question

associe cada equação do 2° grau ás suas respectivas raízes.

Answer 1

Resposta:

a) x² - 3x + 2 = 0

soma e produto: _ + _ = 3

_ . _ = 2

1 + 2 = 3

1.2 = 2

Raízes 1 e 2, alternativa IV.

b) y² - 7y + 12 = 0

soma e produto: _ + _ = 7

_ . _ = 12

3 + 4 = 7

3.4 = 12

Raízes 3 e 4, alternativa I

c) x² - 5x - 6 = 0

soma e produto: _ + _ = 5

_ . _ = -6

-1 + 6 = 5

-1.6 = -6

Raízes -1 e 6, alternativa II

d) Como foi a única que sobrou, alternativa III

Answer 2

Explicação passo-a-passo:

a) $\sf x^2-3x+2=0$

$\sf \Delta=(-3)^2-4\cdot1\cdot2$

$\sf \Delta=9-8$

$\sf \Delta=1$

$\sf x=\dfrac{-(-3)\pm\sqrt{1}}{2\cdot1}=\dfrac{3\pm1}{2}$

$\sf x'=\dfrac{3+1}{2}~\Rightarrow~x'=\dfrac{4}{2}~\Rightarrow~\red{x'=2}$

$\sf x"=\dfrac{3-1}{2}~\Rightarrow~x"=\dfrac{2}{2}~\Rightarrow~\red{x"=1}$

=> Raízes 1 e 2

b) $\sf y^2-7y+12=0$

$\sf \Delta=(-7)^2-4\cdot1\cdot12$

$\sf \Delta=49-48$

$\sf \Delta=1$

$\sf y=\dfrac{-(-7)\pm\sqrt{1}}{2\cdot1}=\dfrac{7\pm1}{2}$

$\sf y'=\dfrac{7+1}{2}~\Rightarrow~y'=\dfrac{8}{2}~\Rightarrow~\red{y'=4}$

$\sf y"=\dfrac{7-1}{2}~\Rightarrow~y"=\dfrac{6}{2}~\Rightarrow~\red{y"=3}$

=> Raízes 3 e 4

c) $\sf x^2-5x-6=0$

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

$\sf \Delta=25+24$

$\sf \Delta=49$

$\sf x=\dfrac{-(-5)\pm\sqrt{49}}{2\cdot1}=\dfrac{5\pm7}{2}$

$\sf x'=\dfrac{5+7}{2}~\Rightarrow~x'=\dfrac{12}{2}~\Rightarrow~\red{x'=6}$

$\sf x"=\dfrac{5-7}{2}~\Rightarrow~x"=\dfrac{-2}{2}~\Rightarrow~\red{x"=-1}$

=> Raízes -1 e 6

d) $\sf t^2+6t+8=0$

$\sf \Delta=6^2-4\cdot1\cdot8$

$\sf \Delta=36-32$

$\sf \Delta=4$

$\sf t=\dfrac{-6\pm\sqrt{4}}{2\cdot1}=\dfrac{-6\pm2}{2}$

$\sf t'=\dfrac{-6+2}{2}~\Rightarrow~t'=\dfrac{-4}{2}~\Rightarrow~\red{t'=-2}$

$\sf t"=\dfrac{-6-2}{2}~\Rightarrow~t"=\dfrac{-8}{2}~\Rightarrow~\red{t"=-4}$

=> Raízes -2 e -4

Logo:

• a) => IV

• b) => I

• c) => II

• d) => III