Question

F(x) = x3 – 13x2 + 52x – 60 Find the roots

Answer 1

Answer:

The roots are 2, 5 and 6.

Step-by-step explanation:

As the last term is 60  we could see if  one root is 2:

2^3 - 13(2)^2 + 52*2 - 60

= 8 - 52 + 104 - 60

= 112 - 112 = 0

So x = 2 is one root and x - 2 is a factor.

Long multiplication:

x - 2 (x^3  - 13x^2  + 52x  - 60 ( x^2 - 11x + 30  <--- Quotient

        x^3  -   2x^2

                 -  11 x^2 + 52x

                 -  11x^2  + 22x

                                   30x - 60

                                   30x - 60

So x^2 - 11x + 30 = 0

(x - 6)(x - 5) = 0

x = 6, 5.