Question

.) Can the Intermediate Value Theorem be applied to show that there is a root of the
equation x^5-x^3+3x - 5 =0 in the given interval ]1,2[? If yes, apply it.​

Answer 1

Answer:

Given f(x)= x^5-x^3+3x-5

now f(1)= 1-1+3-5= -2 <0

f(2) = 32-8+6-5 = 25>0

Here f(1) is Negative

and f(2) is positive

so when we draw the Graph then atleast one time it will cut the X-axis, so there will be atleast one Root of the given Equation...