Question

FIRST ONE TO ANSWER CORRECTLY WILL BE BRAINLIEST

Answer 1

Answer:

b) the coefficient of x of jamie's polynomial is 5 .

c) The two polynomials are :

x³ + 4x² + 5x + 4 

x³ - 2x² + 5x + 4

Step-by-step explanation:

consider these two Monic polynomials of degree 3:

P : x³ + ax² + bx² + c  

Q : x³ + a₁x² + bx² + c  

P × Q = x⁶+ (a+a₁)x⁵ + (aa₁+2b)x⁴ + (ab+a₁b+2c)x³ + (ac+a₁c+b²)x² +2bcx + c²

Now we compare the coefficients of P × Q and  x⁶ + 2x⁵ +2x⁴ + 18x³ + 33x² + 40x + 16

b)

c² = 16 ⇒ c = 4  (c is positive)

2bc = 40 ⇒ 8b = 40 ⇒ b = 5 then the coefficient of x of jamie's polynomial is 5 .

c)

In order to find a and a₁ we need to solve this system:

a+a₁ = 2                   a+a₁ = 2

                      ⇔

aa₁+2b = 2              aa₁ = -8

Solve the system and you’ll get :

a = 4 and a₁ = -2   or a = -2 and a₁ = 4

Let’s choose a = 4 and a₁ = -2 then

the two polynomials are respectively:

P : x³ + ax² + bx² + c  = x³ + 4x² + 5x + 4

Q : x³ + a₁x² + bx² + c  = x³ - 2x² + 5x + 4