Question

Show that 2 and -1/3 are the zero a of the polynomial 3x³-2x²-7x-2.also, find the third zero of the polynomial.

Answer 1

Answer:

- 1

Step-by-step explanation:

Given Show that 2 and -1/3 are the zero a of the polynomial 3x³-2x²-7x-2.also, find the third zero of the polynomial.

Now to show the zero of polynomial : put x = 2 and - 1/3

So let p(x) = 3x³-2x²-7x-2

       p(2) = 3(2)^3 - 2(2)^2 - 7(2) - 2

            = 24 - 24 = 0

Now p(- 1/3) = 3(-1/3)^3 - 2(-1/3)^2 - 7(-1/3) - 2

                  = - 3 + 21 - 18 / 9 = 0

Now we need to find third zero of the polynomial.

So the roots are 2 and - 1/3

We can take (x - 2) and (x + 1/3) as factors

We get 3x^2 - 5 x - 2. Now dividing we get

       3x^2 - 5x - 2) 3 x^3 - 2x^2 - 7 x - 2( x + 1

                              3x^3 - 5x^2 - 2x

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

                                      3x^2 - 5x - 2

                                       3x^2 - 5x - 2

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

                                                0

So x + 1 = 0 or x = -1

So the third zero of the polynomial is - 1