Question

find all the zeros of ( 2x raised to the power 4 -3x cube -5x square + 9x -3 ) it being given that two of its zeros are √3 and -(√3.)

Answer 1

heya..!!!!

given that:-

its zeroes are (√3) AND (-√3)

then,

(x - √3)(x + √3)

=> x² + √3x - √3x - 3

=> (x² - 3)

now,

X²- 3)2x⁴- 3x³ - 5x²+ 9x -3 (2x² - 3x + 1
(-) 2x⁴ (+) -6x²
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
- 3x³ + 1x² + 9x
(+)- 3x³ (-) + 9x
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
x² - 3
x² - 3
¯¯¯¯¯¯¯¯
0 0

now the another zero's is

2x² - 3x + 1

=>2x² - 2x - x + 1

=> 2x(x - 1) - 1(x -1)

=> (2x - 1)(x - 1)

=> x = 1, x = 1/2