SOLUTION: Sketch the graph of a polynomial with odd degree, negative leading coefficient, and zeros x = - 6,(− 5/2) , 1, 4, and 7.

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Question 1156299: Sketch the graph of a polynomial with odd degree, negative leading coefficient, and zeros x = - 6,(− 5/2) , 1, 4, and 7.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Sketch the graph of a polynomial with odd degree,
negative leading coefficient, and
zeros
x%5B1%5D+=+-6
x%5B2%5D+=%28-5%2F2%29+
x%5B3%5D+=1
x%5B4%5D+=4
x%5B5%5D+=7
=> 5 roots, 5 degree
use product of roots theorem
since leading coefficient is negative put minus in front of product of roots



f%28x%29=-%28%28x-%28-6%29%29%28x-%28-5%2F2%29+%29%28x-1+%29%28x-4+%29%28x-7+%29%29

f%28x%29=-%28%28x%2B6%29%28x%2B5%2F2+%29%28x-1+%29%28x-4+%29%28x-7+%29%29....multiply all

f%28x%29=-x%5E5+%2B+7x%5E4%2F2+%2B+48x%5E3+-+247x%5E2%2F2+-+347x+%2B+420...get rid of fraction

f%28x%29=-2x%5E5+%2B+7x%5E4+%2B+96x%5E3+-+247x%5E2+-+694x+%2B+840

graph.png