Answer:
Step-by-step explanation:
Given
Two forces of 9 and 13 lbs acts angle to each other
The resultant of the two forces is given by
Insert the values
Resultant makes an angle of
So, the resultant makes an angle of with 9 lb force
Angle made with 13 lb force is
Using the Factor Theorem, the polynomials are given as follows:
1.
2.
3. P(x) = -0.1(x³ - 4x² - 3x + 18)
<h3>What is the Factor Theorem?</h3>The Factor Theorem states that a polynomial function with roots is given by:
In which a is the leading coefficient.
Item a:
The parameters are:
Hence the equation is:
P(x) = (x - 1)²x²(x + 4)
P(x) = (x² - 2x + 1)(x + 4)x²
P(x) = (x³ + 2x² - 7x + 1)x²
Item b:
The roots are:
Hence:
P(x) = a(x - 4)²x(x + 4)
P(x) = a(x² - 16)x(x - 4)
P(x) = a(x³ - 16x)(x - 4)
It passes through the point x = 5, P(x) = 36, hence:
45a = 36.
a = 4/5
a = 0.8
Hence:
Item 3:
The roots are:
Hence:
P(x) = a(x - 3)²(x + 2)
P(x) = a(x² - 6x + 9)(x + 2)
P(x) = a(x³ - 4x² - 3x + 18)
For the y-intercept, x = 0, y = -1.8, hence:
18a = -1.8 -> a = -0.1
Thus the function is:
P(x) = -0.1(x³ - 4x² - 3x + 18)
More can be learned about the Factor Theorem at brainly.com/question/24380382
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