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yKpoI14uk [10]
3 years ago
9

The question is in the picture.

Mathematics
1 answer:
____ [38]3 years ago
5 0

B. \:\frac{2}{ {a}^{7} } ✅

\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}

\frac{8}{2 \:  {a}^{5} }  \times  \frac{6}{12 \:  {a}^{2} }  \\  =  \frac{48}{24  \:(  {a})^{5 + 2}  }  \\  =  \frac{2}{ {a}^{7} }

<u>Note</u>:-

{a}^{m}  \times  {a}^{n}  =  {a}^{m + n}

\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}

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Read 2 more answers
FIRST ONE TO ANSWER CORRECTLY WILL BE BRAINLIEST
Sunny_sXe [5.5K]

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

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

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3 years ago
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