Question

Find all the zeroes of the polynomial(x4-6x3-26x2+138x-35),it being

given that two of its zeroes are 2 + √3 and 2-√3​

Answer 1

Answer:

given two zeroes of polynomial are 2+(3)½,2-(3)½

=> x-(2+root3) ,x-(2-root3) are factors of polynomial

=>[x-2-(3)½][x-2+(3)½]=(x-2)²-3

=x²-4x+4-3

=x²-4x+1

=>x²-4x+2)x⁴-6x³-26x²+138x-35(x²-2x-36

x⁴-4x³+2x²

(-) (+) (-)

____________________

-2x³-28x²+138x

-2x³+ 8x²- 4x

(+) (-) (+)

____________________

-36x²+142x-35

-36x²+144x-72

(+) (-) (+)

_____________________

-2x+37

=>x²-2x-36=0

=>x=2+(4+144)½÷2,2-(4+144)½÷2

=1+(37)½,1-(37)½