Final answer:
To find the real solutions of the equation x^(3) + 9x^(2) + 11x + 21 = 0 using the x-intercept method, we can factor or use synthetic division to find the x-intercepts.
Step-by-step explanation:
To find the real solutions of the equation x^(3) + 9x^(2) + 11x + 21 = 0 using the x-intercept method, we can factor or use synthetic division to find the x-intercepts. Since this equation is a cubic equation, we will use synthetic division to find the x-intercepts.
The x-intercepts are the values of x where the equation intersects the x-axis.
We substitute different values for x until we find one that makes the equation equal to zero.
The values of x that make the equation equal to zero are the x-intercepts or the real solutions of the equation.
Using synthetic division, we find that x = -7, -3, and -1 are the real solutions of the equation.