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

They are - 1, 4 and 7.

Step-by-step explanation:

x^3 - 10x^2 + 17x + 28 = 0

Observation of this equation shows that there is an x - intercept at x = - 1 because

-1^3 - 10^ (-1) ^2 - 17 (1) + 28 = - 28 + 28

= 0.

So x + 1 must be a factor so we can do the division:

x + 1) x^3 - 10x^2 + 17x + 28 (x^2 - 11x + 28

x^3 + x^2

-11x^2 + 17x

-11x^2 - 11x

28x^2 + 28

x^2 - 11x + 28 = (x - 4) (x - 7)

x = 4, 7.