Question

find all the zeroes of the polynomial 2x⁴-3x³-5x²+9x-3 ​

Answer 1

Step-by-step explanation:

Let f(x)=2x−3x−5x+9x−3

Given under root 3 and under root − 3 are the zeros of the polynomial.

(x− under root 3 ) and (x+under root 3) are factors f(x)

So (x−under root 3) (x+under root 3) = (x²-3) is a factor

f(x)

Divide f(x) by (x²−3)

set f(x)=0

(2x²−3x+1)(x²-3) = 0

2x²−3x² −5x² +9x−3=0

(x² -3)(2x²−3x+1)=0

(x² -3)(2x²−2x−x+1)=0

(x²- 3 )(x+ 3 )(2x−1)(x−1)=0

either x= under root 3 or x=− under root 3 or x= 1/2 or x=1

Hence , all the zeros of the given polynomial are underoot 3, underoot -3 , 1/2 and 1