Question

1- Seja p(x)= x2-6x+5
Calcule:

A) P (5)
B) P (x)=0

2- Calcule o valor de "k"
Pa=x2+kx+3 5e F (2)=9

Answer 1

1)

p(x) = x² - 6x + 5

a)

p(5) = 5² - 6.5 + 5

p(5) = 25 - 30 + 5

p(5) = 30 - 30

p(5) = 0

b)

p(x) = 0

x² - 6x + 5

Δ = b² - 4.a.c  

Δ = -6² - 4 . 1 . 5  

Δ = 36 - 4. 1 . 5  

Δ = 16

Há 2 raízes reais.

x = (-b +- √Δ)/2a

x' = (--6 + √16)/2.1    

x'' = (--6 - √16)/2.1

x' = 10 / 2    

x'' = 2 / 2

x' = 5    

x'' = 1

p(5) e p(1) é igual a 0.

2)

f(x) = x² + kx + 3

f(2) = 9

f(2) = 2² + k.2 + 3

f(2) = 4 + 2k + 3

f(2) = 2k + 7

f(2) = 9

2k + 7 = 9

2k = 9 - 7

2k = 2

k = 2/2

k = 1

f(x) = x² + 1.x + 3

f(x) = x² + x + 3