Final answer:
To find the real solutions of the equation x^3-8x^2+17x-10=0 using the x-intercept method, factor the equation and set each factor equal to zero. The real solutions are x=2, x=1, and x=5.
Step-by-step explanation:
To find the real solutions of the equation x^3-8x^2+17x-10=0 using the x-intercept method, we need to find the x-values where the graph of the equation intersects the x-axis. This is done by factoring the equation and setting each factor equal to zero.
Step 1: Factor the equation: (x-2)(x-1)(x-5)=0
Step 2: Set each factor equal to zero and solve for x:
- x-2=0 ➔ x=2
- x-1=0 ➔ x=1
- x-5=0 ➔ x=5
Therefore, the x-intercepts or real solutions of the equation are x=2, x=1, and x=5.