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
Answer:
2/5
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(2-6)/(-6-4)
m=-4/-10
simplify
m=2/5
Measure of the smaller angle is 75°
Step-by-step explanation:
- Step 1: Sum of supplementary angles is 180°. Given ratio of angles is 5:7.
Let angles be 5x and 7x.
⇒ 5x + 7x = 180
⇒ 12x = 180
⇒ x = 15
- Step 2: Calculate smaller angle which is 5x
⇒5x = 5 
15 = 75°
Use this. It’s really good
Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.
