Question

find all the zeros of the polynomial 2 x 4 - 9 x cube + 5 x square + 3 x minus 1 if two of its zeros are 2 + root 3 and 2 minus root 3

Answer 1

x = 2 + root3 and x = 2 - root3

these are the zeros of P(x)

( x - 2 - root3 ) ( x - 2 + root3 )

by using formula we know,

( a - b ) ( a +b ) = a^2 - b^2

so now,

( x - 2 )^2 - ( root3 )^2

x^2+ 4 - 4x - 3=0

x² + 1 - 4x ( a)

When we have to  divide P( x ) by  equation a we will get the zero, that is

x=1, and x=-1/2