Find the third zero if two of itz zeroes are 2 and 3

Question

X³-6x²+11x-6 is the p(x)

Answer 1

p(x) = x³ - 6x² + 11x - 6

 

Zeroes at x = 2, x = 3

If there is a zero at x=2 then (x-2) is a factor

If there is a zero at x=3 then (x-3) is a factor

 

(x-2)(x-3)(y) = x³ - 6x² + 11x - 6

 

y = (x³ - 6x² + 11x - 6)/[(x-2)(x-3)]

 

y = (x³ - 6x² + 11x - 6)/(x² - 5x + 6)

 

 

                x - 1

             -------------------------------

x²-5x+6 |  x³ - 6x² + 11x - 6

              -(x³ - 5x² + 6x)

             --------------------------

                    -x² + 5x - 6

                 -(-x² + 5x - 6)

                -------------------

                                   0

 

The final factor of the polynomial is (x-1)

The 3rd zero is at x = 1

 

 

p(x) = (x-1)(x-2)(x-3) = x³ - 6x² + 11x - 6

Answer 2

Then x^2 - 5x + 6 is a factor

 

 

Dividing p(x) by this quadratic results in a quotient of x-1

 

So X=1 is the third zero.

 

Note that p(1) = 0