Answer:
In the picture above
Step-by-step explanation:
I hope that it's a clear solution and explanation.
Goodluck.
PLEASE HELP MATH 10+ POINTS PLEASE
2 answers:
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Answer:
- p(x) = x³ +0x² +0x +0
- p(x) = x³ +x² -x -1
- p(x) = x³ -x² -2x
Step-by-step explanation:
If the roots of p(x) are a, b, c, then it factors as ...
p(x) = (x -a)(x -b)(x -c)
and the expanded form is ...
p(x) = x^3 -(a+b+c)x^2 +(ac +b(a+c))x -abc
The requirement that the coefficients match the roots means we have three equations in three unknowns:
a = -(a+b+c)
b = ac +b(a+c)
c = -abc
The attachment shows the solutions to these equations. The solutions are found by making the substitutions ...
- b = x
- c = y
- a = -(x+y)/2
This leaves us with two equations in two unknowns that can be graphed on a Cartesian plane. The graph of the second equation is a circle:
x(1 -a -y) -ay = 0 ⇒ (x +1)^2 +y^2 = 1
The graph of the first equation is the union of the line y=0 and two hyperbolas. The points of intersection between this graph and the circle are ...
(x, y) = (-2, 0), (-1, -1), (0, 0) ⇒ (a, b, c) = (1, -2, 0), (1, -1, -1), (0, 0, 0)
The three polynomials that correspond to these values are shown above and in the attachment.
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<em>Additional comment</em>
There is an irrational fourth solution to the requirement that the roots match the coefficients.
Answer:
28. (H) 24 ft
30. (F)
Step-by-step explanation:
28. A right triangle can be formed, where the length of the cable represents the hypotenuse, and the ground represents the base of the triangle. From the pythagorean theorem,
where a and b are legs, and c is the hypotenuse of a right triangle.
So
30. The probability of drawing a red 1 is (a red star 1 or a red heart 1), the probability of drawing a black 3 is
(a black triangle 3 or a black circle 3), and the probability of drawing a six of hearts is
(since there is only one six of hearts in the entire deck). Since each of the cards is mutually exclusive from one another, the probability of drawing any of them is simply all of their probabilities added together. That is,