Question

Please give written solutions of question no 10

Answer 1

Step-by-step explanation:

Given polynomial is f(x) = x³ + 3x² - 2x - 6.

Given, zeroes are √2 and -√2.

Since, two zeroes are √2 and -√2,

So, (x - √2)(x + √2) = x² - 2 is a factor of the given polynomial.

Now, we divide the given polynomial by x² - 2 to obtain other zeroes.

Long Division Method:

x² - 2) x³ + 3x² - 2x - 6 (x + 3

          x³          - 2x

          ----------------------

                      3x²  - 6

     

                      3x²  - 6

           ---------------------

                          0

So, x³ + 3x² - 2x - 6 = (x² - 2)(x + 3)

So, its zeroes are -3.

Therefore, the zeroes of the polynomial are: √2, -√2, -3.

Hope it helps!

Answer 2

Answer:

x^2-2)_x3+3x2-2x-6______(

            x3         -2x

           -              +

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

            3x^2        -6

             3x^2       -6

             -             +

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

                   0

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

x3+3x2-2x-6

=(x^2-2)(x+3)

=±√2,3