find the other zeroes of the polynomial x4 - 7x2 + 12if it is given that two of its zeroes root3 and -root3.

P (x) = x^4 - 7x^2 + 12

The zeros are root 3 and -root 3

=(x- root 3) (x + root 3) is a factor of the equation!

= ( x^2 -3) is a factor

x^4 - 7x^2 + 12 divided by x^2 - 3 = x^2 - 4 (division method)

P (x) = [g (x) × q (x)] + r (x)

x^4 - 7x^2 +12 =[( x^2 -3 ) ÷ (x^2 -4)] + 0

x^2 - 4 = x^2 -0x - 4 = x^2 +2x - 2x -4 = x ( x+2) - 2 (x+2) = (x-2) (x+2)

= x-2 = 0, x= 2

= x+2 = 0, x = -2

Therefore, the zeros are root 3, - root 3, 2 and -2.