Question

Where does the one root of the equation `x^3-3x^2+4x-1=0` lie between? a) 0 and 1 b) 1 and 2 c) 2 and 3 d) 4 and 5

Answer 1

One root lies between `0 and 1`

Explanation:

`x^3-3x^2+4x-1=0`

Let `f(x) = x^3-3x^2+4x-1`

`f(0)=0^3-3*0^2+4*0-1 = -1 >> (-)`

`f(1)=1^3-3*1^2+4*1-1 = 1 >> (+ ) ;` (change of sign)

`f(2)=2^3-3*2^2+4*2-1 = 3 >> (+ ) ;`

`f(3)=3^3-3*3^2+4*3-1 = 11 >> (+ ) ;`

`f(4)=4^3-3*4^2+4*4-1 = 31 >> (+ ) ;`

`f(5)=5^3-3*5^2+4*5-1 = 69 >> (+ ) ;`

Change of sign occurs between `0 and 1` only , so one

root lies between `0 and 1` [Ans]