Question

Show that the equation x^3 + x - 3 has a solution between 1 and 2

Answer 1

see explanation

Explanation:

Evaluate the polynomial at x = 1 and x = 2

x = 1 : 1³ + 1 - 3 = 1 + 1 - 3 = - 1

x = 2 : 2³ + 2 - 3 = 8 + 2 - 3 = 7

Then ( 1, - 1 ) → (2, 7 )

Shows the polynomial goes from y = - 1 to y = + 7

The change in sign indicates the graph crosses the x- axis between 1 and 2

Thus indicating a solution between x = 1 and x = 2