F(-1)....this is basically saying that x = -1...and when x = -1 (according to ur chart), then f(-1) = 0 <==
Answer: True
Explanation:
According to the rational zeros theorem, if x=a is a zero of the function f(x), then f(a) = 0.
Given: f(x) = x⁴ + x³ - 11x² - 9x + 18
From the calculator, obtain
f(5) = 448
f(4) = 126
f(3) = 0
f(2) = -20
f(1) = 0
f(0) = 18
f(-1) = 16
f(-2) = 0
f(-3) = 0
The polynomial is of degree 4, so it has at most 4 real zeros.
From the calculations, we found all 4 zeros as x = -3, -2, 1, and 3.
Therefore
f(x) = (x+3)(x+2)(x-1)(x-3).
For x>3, f(x)increases rapidly. Therefore there are no zeros for x>3.
The statement that x=5 is an upper bound for the zeros of f(x) is true.
Answer:
a) 40
b) 80
c) 77
d) 48
Step-by-step explanation:
To find the missing numerator, multiply the equation by the denominator of the fraction with the missing numerator.
a) (10/15)(60) = (x/60)(60)
40 = x
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b) (x/180)(180) = (4/9)(180)
x = 80
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c) (7/11)(121) = (x/121)(121)
77 = x
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d) (x/144)(144) = (2/6)(144)
x = 48
Answer:
I'm pretty sure its D. 11.5
Using the quadratic equation instead of calculus, you can find the x coordinate of the vertex as it will be the midpoint of the two x coordinates of the zeros...
x=(-3±√-27)/2
x=-1.5±√-6.75
That the second term is imaginary does not matter because we will add or subtract this value from -1.5, thus the midpoint of the zeros, the x coordinate of the vertex is -1.5. And to find the value of y for the vertex we just find the value of y when x=-1.5
y(-1.5)=6.75
Since y>0, the vertex is above the x-axis.
