Question

I need the solution pls answer...​

Answer 1

at first you have to make the sum and product

then divide the polynomial by given polynomial

Answer 2

Step-by-step explanation:

Two zeroes are √3 and -√3,

Therefore (x -√3)(x - (-√3) = (x - √3)(x + √3) is a factor of p(x).

Let us divide p(x) by (x - √3)(x + √3)

=> (x² - 3)

Long Division Method :

x²-3) 2x⁴ - 3x³ - 5x² + 9x - 3 (2x²-3x+1

         2x⁴           - 6x²

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

                     -3x³   + x²  +  9x - 3

                     - 3x³           + 9x

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

                                  x²   -  3

                                  x²   -  3

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

                                  0

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

Now,

(2x⁴-3x³-5x²+9x-3) = (x²-3)(2x²-3x+1)

= (x-√3)(x+√3)(2x²-2x-x+1)

= (x-√3)(x+√3)(2x(x-1)-1(x-1))

= (x - √3)(x + √3)(2x - 1)(x - 1)

Hence,

2x - 1 = 0 or x - 1 = 0

x = (1/2) , 1

Hence, other two zeroes are (1/2) ,1

Hope it helps!