Question

Obtain all the zeros of p(x) = 3 x ^4 + 6 x^ 3 - 2 x ^2 - 10 x - 5 if two of its zeros are - 1 and 1​

Answer 1

Equation=3x^4+6x^3-2x^2-10x-5

Factor 1=(x+1)

Factor 2=(x-1)

Dividing Equation by Factor 1=3x^3+3x^2-5x-5  //Root of this = -1

Dividing Equation by Factor 2=3x^3+9x^2+7x-3

Equation 2 gives its root as -1

Now we can also factor the original equation=

(x+1)^2(3x^2-5)=0

Therefore:

Root 3= -(sqrt(5/3))

Root 4= sqrt(5/3)

However the root (1) seems to be wrong, it leaves -8 as remainder when we divide the original equation by (x-1)

Therefor we see only 3 roots=

Root 1=-1

Root 2= -(sqrt(5/3))

Root 3= sqrt(5/3)