Question

Find all the zeros pf the polynomial 2x^4 - 9x^3 + 5 x^2 + 3x - 1 of two of its zeros are 2+√3 and 2-√3

Answer 1

Since 2+√3 and 2-√3 are the roots

Therefore (x-2-√3) and (x-2+√3) will be factors of the given polynomial.

(2x⁴ -9x³ +5x²+3x-1) = (x-2-√3)(x-2+√3) .g(x)

Now simply dividing (2x⁴ -9x³ +5x²+3x-1) by

(x-2-√3) (x-2+√3) = (x-2)² - 3 = x²–4x+1

(2x⁴ -9x³ +5x²+3x-1) / (x²–4x+1)

=( 2x²-x-1)

Therefore g(x)= 2x²-x-1 =( x-1) (2x+1).

Therefore other two roots are 1, -1/2 .Since 2+√3 and 2-√3 are the roots

Therefore (x-2-√3) and (x-2+√3) will be factors of the given polynomial.

(2x⁴ -9x³ +5x²+3x-1) = (x-2-√3)(x-2+√3) .g(x)

Now simply dividing (2x⁴ -9x³ +5x²+3x-1) by

(x-2-√3) (x-2+√3) = (x-2)² - 3 = x²–4x+1

(2x⁴ -9x³ +5x²+3x-1) / (x²–4x+1)

=( 2x²-x-1)

Therefore g(x)= 2x²-x-1 =( x-1) (2x+1).

Therefore other two roots are 1, -1/2 .

Answer 2

Answer:

Hope this helps you ✌️✌️