Find all zeros of the polynomial g(x)=x^4-9x^2-4x+12?

zeros-of-polynomial

#1

find all zeros of the polynomial g(x)=x^4-9x^2-4x+12?

Answer:

g(x) = x^4 - 9x^2 - 4x + 12
= (x-1) (x^3) + x^3 + (x-1) (-9x) -9x +(x-1) (-4) -4 +12
=(x-1)(x^3 - 9x -4) + x^3 -9x +8
= (x-1) (x^3 -9x - 4) + (x-1) (x^2) + x^2 + (x-1) (-9) -9 +8
= (x-1) (x^3 -9x - 4) + (x-1) (x^2-9) + x^2 -1
=(x-1) (x^3 -9x - 4) + (x-1) (x^2-9) + (x-1) (x+1)
= (x-1) (x^3 + x^2 -8x -12)
= (x-1) [ (x-3) (x^2+4x + 4)
= (x-1) (x-3) (x+2) (x+2)
Hence zeros are: 1, 3, -2 and -2