Answer:
x^4 - 14x^2 - 40x - 75.
Step-by-step explanation:
As complex roots exist in conjugate pairs the other zero is -1 - 2i.
So in factor form we have the polynomial function:
(x - 5)(x + 3)(x - (-1 + 2i))(x - (-1 - 2i)
= (x - 5)(x + 3)( x + 1 - 2i)(x +1 + 2i)
The first 2 factors = x^2 - 2x - 15 and
( x + 1 - 2i)(x +1 + 2i) = x^2 + x + 2ix + x + 1 + 2i - 2ix - 2i - 4 i^2
= x^2 + 2x + 1 + 4
= x^2 + 2x + 5.
So in standard form we have:
(x^2 - 2x - 15 )(x^2 + 2x + 5)
= x^4 + 2x^3 + 5x^2 - 2x^3 - 4x^2 - 10x - 15x^2 - 30x - 75
= x^4 - 14x^2 - 40x - 75.
Rearranging y = 8x -4y = 12 in the y = mx + b form gives y = 2x - 3
y = 2x - 3
y = mx - 6 (already in y = mx + b form)
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Parallel lines have the same slope.
m = 2
Note that the two lines have the different y-intercepts and are not the same line.
Answer:
Equilateral triangles are sometimes
acute triangles.
Scalene triangles are never
acute triangles.
Right triangles are never
acute triangles.
Obtuse triangles are always
isosceles triangles.
The answer to this is : 0.75 (.75)
