Question

Use the x-intercept method to find all real solutions of the equation x^3-10x^2+17x+28=0

Answer 1

x = -1, x = 4 and x = 7

Explanation:

x-intercept method consists in plotting the equation, in this case x^3-10x^2+17x+28, and see where the graph intersects the x-axis. These are the points where for a given value of x, y = 0, and they are called the solutions of the equation. In this case these points are: x = -1, x = 4 and x = 7 (see figure attached).

Answer 2

A graphing calculator shows the x-intercepts of the expression on the left to be -1, 4, 7.

The real solutions to the cubic equation are x ∈ {-1, 4, 7}.