Question

Solve the equation x
³
– 13x
²+ 15x + 189 = 0,Given that one of the roots

exceeds the other by 2.​

Answer 1

Answer: x1=7 x2=9 x3=-3

Step-by-step explanation: suppose that x1 is one of the root, x1+2 will be root too:

1) put (x1)^3-13(x1)^2+15x1+189=(x1+2)^3-13(x1+2)^2+15(x1+2)+189 => x1=-1/3 ; x1=7

x1=-1/3 isn't a root, so roots are x1=7 and x2=x1+2=9

Let's divide equation by (x-7)(x-9) (Horners method),we will get (x+3), so x3=-3 is a root too.