Use the x-intercept method to find all real solutions of the equation. x^3-8x^2+17x-10=0

f(2)  = 8 - 32 + 34 - 10 =  0

so one real solution is x = 2 and x - 2 is a factor.,

Dividing  the function by x -2 gives

x^2 - 6x + 5 

x^2 - 6x + 5 = 0

(x - 5)(x - 1) = 0  

x = 1 , 5

All real roots are 1,2 and 5.