Question

can I get help on this question
Show that there is a root of the equation
4x^3-6x^2+3x-2
between 1 and 2
how can I do it?

Answer 1

if f(1) and f(2) are opposited signs; then that means it crossed over someplace between them right?

Answer 2

let equation =y.
on substituting x=1, we get y=negative
on substituting x=2, we get y=positive.
So the curve of given equation passes from -Y side to +Y side for values starting from x=1 till x= 2.
Means a root must lie between x=1 and 2 for which the curve intersects y=0.

Answer 3

in other words; if you start out on one side of the road, and you end up on the other side; that means you had to have crossed over at some point in between...