Question

Obtain all the zeroes of polynomial x4-3x3-x2+9x-6 . If two zeroes are -√3 and√3

Answer 1

Step-by-step explanation:

p(x)= x4-3x3-x2+9x-6

it's two zeroes are... -✓3,✓3

(x-✓3) [x-(-✓3)]is the factor of p(x)

(x-✓3) (x+✓3)is the factor of p(x)

x^2 - (✓3)^2is the factor of p(x)

(x^2-3)is the factor of p(x)

on dividing p(x) by (x^2-3),we get

p(x)= x4-3x3-x2+9x-6 =(x^2-3) (x^2-3x+2)

for other zeroes ......

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

x^2-2x-x+2=0

x(x-2) -1(x-2)=0

(x-2) (x-1)=0

x= 2 and x=1

Hence all the zeroes of p(x)= -√3 ,√3 ,2 ,1

hope it helps you