Find all rational zeros of the polynomial P(x)=4x4−6x3−6x−4 Its rational zeros are x1= ? , x2= ? , x3= ? and x4= ? with x1≤ x2 ≤x3 ≤x4

Answer 1

Solution:

P(x)=4x4-6x3-6x-4

4x4-4-6x3-6x

=4(x4-1)-6x(x2-1)

=4(x2+1)(x2-1)-6x(x2-1)

=(x2-1){4(x2+1)-6x}

=(x+1)(x-1){4x2+4-6x}

=(x+1)(x-1) 2(2x^2 - 3x+ 2) =0

=2(x+1) (x-1)

Here x is equal to -1 and 1