Answer:
False
Step-by-step explanation:
We are given that the number 1 is an upper bound for the set of roots of this polynomial function
[tex]f(x)=3x^4-5x^3-5x^2+5x+2[/tex]
We have to find the statement is false or true.
Substitute x=1 then we get
[tex]f(x)=3(1)-5(1)-5(1)+5(1)+2[/tex]
[tex]f(x)=3-5-5+5+2=0[/tex]
Hence, 1 is the root of the given polynomial
Now substitute x=2 then we get
[tex]f(x)=3(2)^4-5(2)^3-5(2)^2+5(2)+2[/tex]
[tex]f(x)=48-40-20+10+2=60-60=0[/tex]
Hence, 2 is also root of the given polynomial .
Upper bound: It is defined as the highest value of the set and all values in the set are less than the upper bound .
Here we have find two roots but 2 is greater than 1 . So 1 is not the upper bound for the set of roots of polynomial .
Hence, it is false.
Answer : False
