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cluponka [151]
2 years ago
11

The illustration below is a graph of the polynomial function P(x). The graph crosses the x-axis 2 times and touches the x-axis o

nce at the point (4, 0).
Part A: Use the key features of the graph to explain that the degree of the polynomial cannot be odd.

Part B: How many unique zeros does this polynomial have?

Mathematics
1 answer:
Anastaziya [24]2 years ago
4 0
The polynomial graph crosses the x-axis at two points and touches x-axis at one point. It indicates the graph has four roots:

x=-1.5
x=-2
x=4
x=4

The last two roots have equal value as the graph touches the x-axis (not crosses it)

The graph has three unique roots

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Ostrovityanka [42]

Hello from MrBillDoesMath!

Answer:

See Discussion below

Discussion:

A function f is even if f(-x) = f(x)


f(x)                               f(-x)                                  Are they equal?

----------------------------------------------------------------------------------------

-x^8 + 2x^6-5x           -(-x)^8 + 2(-x)^6 + 5x         No

3 abs(x) - 4                 3 abs(-x) -4                       Yes

log5 x^2                     log5 (-x)^2                        Yes

(6x)^ (1/7)                     (-6x)^(1/7)                          No

e^(x^2-x)                     e^( (-x)^2+x)                      No

(x^8 +5x^2)^(-1)           ( (-x)^8 + 5 (-x)^2) ^(-1)      Yes


Answers with Yes, above are even functions.

Regards,  

MrB

P.S.  I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!


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