Step-by-step explanation:
if (2 + √3) & (2 - √3) are two Zeroes
=> (x - (2 + √3))(x - (2 - √3)) is a factor of 2x⁴ - 9x³ + 5x² + 3x - 1
x² -x(2 + √3 + 2 - √3) + (4 - 3)
= x² - 4x + 1
2x² - x -1
x² - 4x + 1 _| 2x⁴ - 9x³ + 5x² + 3x - 1 |_
4x⁴ - 8x³ + 2x²
_________________
-x³ + 3x² + 3x - 1
-x³ + 4x² - x
________________
-x² + 4x - 1
-x² + 4x - 1
____________
0
2x⁴ - 9x³ + 5x² + 3x - 1 = ( x² - 4x + 1) (2x² - x -1)
2x² - x -1 = 0
=> 2x² - 2x + x - 1 = 0
=> 2x(x - 1) + 1(x - 1) = 0
=> (2x + 1)(x - 1) = 0
=> x = -1/2 & x = 1
