Question

obtain all zeros of 3 x to the power 4 - 15 x cube + 13 x square + 25 x minus 30 if two of its zeros are under root 5 by 3 and minus under root 5 by 3 short answer

Answer 1

Answer:

Step-by-step explanation:

x-√5/3 and. x+√5/3

(x-√5/3) (x+√5/3) (x- alpha) (x-beeta)=3x^4+6x^3-2x^2-10x-5

(x^2-5/3) (x-alpha) (x- beeta)= 3x^4+6x^3-2x^2-10x-5

(x-alpha) (x-beeta)= 3x^4-6x^3-2x^2-10x-5/x^2-(5/3)

(x-alpha) (x-beeta)= 3x^2+6x+3

=3(x^2+2+1)

from the identity a^2+b^2+2ab=(a+b)^2

(x-alpha) (x-beeta)= 3(x+1)(x+1)

(x-alpha)= x+1. (x-beeta)=x+1

x-x- alpha=1. x-x-beeta=1

alpha=-1. beeta=-1