Answer:
b.(-2, -1), (3, 4)
Step-by-step explanation:
We are given function as
[tex]f(x)=x^4-3x^3-2x^2+3x-5[/tex]
We can verify each intervals
At (-6,-5):
Firstly we will plug x=-6
[tex]f(-6)=(-6)^4-3(-6)^3-2(-6)^2+3(-6)-5=1849[/tex]
now, we can plug x=-5
[tex]f(-5)=(-5)^4-3(-5)^3-2(-5)^2+3(-5)-5=930[/tex]
since, both are positive values
So, zeros can not lie between them
At (-4,-3):
Firstly we will plug x=-4
[tex]f(-4)=(-4)^4-3(-4)^3-2(-4)^2+3(-4)-5=399[/tex]
now, we can plug x=-3
[tex]f(-3)=(-3)^4-3(-3)^3-2(-3)^2+3(-3)-5=130[/tex]
since, both are positive values
So, zeros can not lie between them
At (-2,-1):
Firstly we will plug x=-2
[tex]f(-2)=(-2)^4-3(-2)^3-2(-2)^2+3(-2)-5=21[/tex]
now, we can plug x=-1
[tex]f(-1)=(-1)^4-3(-1)^3-2(-1)^2+3(-1)-5=-6[/tex]
since, one is positive and another is negative
So, zeros will lie between them
At (3,4):
Firstly we will plug x=3
[tex]f(3)=(3)^4-3(3)^3-2(3)^2+3(3)-5=-14[/tex]
now, we can plug x=4
[tex]f(4)=(4)^4-3(4)^3-2(4)^2+3(4)-5=39[/tex]
since, one is positive and another is negative
So, zeros will lie between them
zeros will be between
(-2, -1), (3, 4)
