1.

Show that the root of Equation x^3-6x+3=0 lies between 2 and 3

Answer»

Given equation is x3 - 6x + 3 = 0

let f(x) = x3 - 6x + 3

Now, f(2) = 23 - 6 x 2 + 3

= 8 - 12 + 3

= 11 - 12 

= -1<0

And f(3) = 33 - 6 x 3 + 3

= 27 - 18 + 3

= 12 > 0

Thus, f(2) f(3) > 0

Therefore, the root of the equation x3 - 6x + 3 = 0 lies between 2 and 3



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