Change of sign method

Question 1

What are the steps for this question:
“Show that the equation 0.2x^3 = 5x(x+2), has a root between -2 and -1”

Answer 1

1)let the equation equal 0, get everything onto one side
2)get it into function notation (let f(x) = the equation)
3)sub the values given in the question into f(x)
4)write statement

Question 2

What statement should you write at the end of the answer?

Answer 2

there is a change in sign, and f(x) is continuous between __ and __
therefore there must be a root between _ and _

Question 3

Show that the equation 0.2x^3 = 5x(x+2), has a root between -2 and -1

Answer 3

0.2x^3 - 5x(x+2) = 0
f(x) = 0.2x^3 - 5x(x+2)
f(-2) = -8/5 <0
f(-1) = 24/5>0
(one is - and one is + so we have a change in sign)
there is a change in sign, and f(x) is continuous between -2 and -1
therefore there must be a root between -2 and -1