Question

1- determine a raiz de P(x)=8x-16?
2-Dado o polinômio P(x)=5x³+2x+1, calculando P(2), encontramos:
3-Dado o polinômio P(x)=2x³+x²+1, calculando P(1)-2P(3)
4Dado o polinômio P(x)=x³+3x²+3, calculando P(2/3):

Answer 1

• 1) Iguale a zero e resolva.

• 2) Substitua x por 2 e resolva.

• 3) Substitua x por 1 e 3, depois resolva.

• 4) Substitua x por 2/3 e resolva.

1)

8x - 16 = 0

8x = 16

x = 16/8

x = 2

2)

P(x) = 5x³ + 2x + 1

P(2) = 5 . 2³ + 2 . 2 + 1

P(2) = 5 . 8 + 4 + 1

P(2) = 40 + 5

P(2) = 45

3)

P(x) = 2x³ + x² + 1

P(1) = 2 . 1³ + 1² + 1

P(1) = 2 . 1 + 1 + 1

P(1) = 2 + 2

P(1) = 4

P(3) = 2 . 3³ + 3² + 1

P(3) = 2 . 27 + 9 + 1

P(3) = 54 + 10

P(3) = 64

P(1) - 2P(3) = 4 - 2 . 64

P(1) - 2P(3) = 4 - 128

P(1) - 2P(3) = - 124

4)

P(x) = x³ + 3x² + 3

P(2/3) = (2/3)³ + 3 . (2/3)² + 3

P(2/3) = 8/27 + 3 . 4/9 + 3

P(2/3) = 8/27 + 12/9 + 3

P(2/3) = 8/27 + 36/27 + 81/27

P(2/3) = 44/27 + 81/27

P(2/3) = 125/27

Resposta:

1) 2

2) 45

3) - 124

4) 125/27

Answer 2

Explicação passo-a-passo:

1)

A raiz de um polinômio, $\sf P(x)$, é o valor de $\sf x$ tal que $\sf P(x)=0$

$\sf 8x-16=0$

$\sf 8x=16$

$\sf x=\dfrac{16}{8}$

$\sf \red{x=2}$

A raiz desse polinômio é 2

2)

$\sf P(x)=5x^3+2x+1$

=> Para x = 2:

$\sf P(2)=5\cdot2^3+2\cdot2+1$

$\sf P(2)=5\cdot8+4+1$

$\sf P(2)=40+4+1$

$\sf \red{P(2)=45}$

3)

$\sf P(x)=2x^3+x^2+1$

$\sf \Rightarrow~P(1)$

• Para x = 1:

$\sf P(x)=2x^3+x^2+1$

$\sf P(1)=2\cdot1^3+1^2+1$

$\sf P(1)=2\cdot1+1+1$

$\sf P(1)=2+1+1$

$\sf \red{P(1)=4}$

$\sf \Rightarrow~P(3)$

• Para x = 3:

$\sf P(x)=2x^3+x^2+1$

$\sf P(3)=2\cdot3^3+3^2+1$

$\sf P(3)=2\cdot27+9+1$

$\sf P(3)=54+9+1$

$\sf \red{P(3)=64}$

Assim:

$\sf P(1)-2\cdot P(3)=4-2\cdot64$

$\sf P(1)-2\cdot P(3)=4-128$

$\sf \red{P(1)-2\cdot P(3)=-124}$

4)

$\sf P(x)=x^3+3x^2+3$

=> Para $\sf x=\dfrac{2}{3}$:

$\sf f\Big(\dfrac{2}{3}\Big)=\Big(\dfrac{2}{3}\Big)^3+3\cdot\Big(\dfrac{2}{3}\Big)^2+3$

$\sf f\Big(\dfrac{2}{3}\Big)=\dfrac{8}{27}+3\cdot\dfrac{4}{9}+3$

$\sf f\Big(\dfrac{2}{3}\Big)=\dfrac{8}{27}+\dfrac{12}{9}+3$

$\sf f\Big(\dfrac{2}{3}\Big)=\dfrac{8+12\cdot3+3\cdot27}{27}$

$\sf f\Big(\dfrac{2}{3}\Big)=\dfrac{8+36+81}{27}$

$\sf \red{f\Big(\dfrac{2}{3}\Big)=\dfrac{125}{27}}$