Question

if two zeros of the polynomial
$(x) = 2x {}^{4} - 3x {}^{ 3} + 6x - 2$
are
$\sqrt{2 \: }$
and
$\sqrt{ - 2}$
find its other two zeros​

Answer 1

Zeroes are  1/2 ,  1  , √2 , - √2 , if √2 and  - √2 are Two zeroes  of 2x⁴  - 3x³  - 3x²  + 6x  - 2

Step-by-step explanation:

Two zeroes are  √2  & - √2

(x - √2)(x + √2)

= x² - 2

(2x⁴  - 3x³  - 3x²  + 6x  - 2)/(x² - 2)

= (2x²  - 3x  + 1)

2x²  - 3x  + 1 = 0

=> 2x² - 2x - x + 1 = 0

=> 2x(x - 1) - 1(x - 1) =0

=> (2x - 1)(x - 1) = 0

=> x = 1/2  or 1

Zeroes are  1/2 ,  1  , √2 , - √2