Question

Obtain all the zeros of 2x⁴-2x³-7x²+3x+6 if [x±√4/2]are two factors of this polynomial

Answer 1

Answer:

Step-by-step explanation:

Method of finding the remaining zeros of a polynomial when sum of  its zeros are given:

We firstly write the factor of polynomial using given zeros and multiply them to get g(x). Then divide a given polynomial by g(x).

The quotient so obtained give other zeros of given polynomial and we factorise it to get other zeros.

SOLUTION:

Let f(x) = 2x⁴  – 2x³  –7x²  + 3x  + 6

Given :

(x+√3/2) & (x-√3/2) are the two factors of given Polynomial f(x).

(x+√3/2) (x-√3/2)

= x²- 3/2 = (2x²-3)/2

= (2x²-3)/2=0

2x²-3 is a factor of given Polynomial f(x)

Divide f(x) =2x⁴  – 2x³  –7x²  + 3x  + 6 by 2x²-3

[DIVISION IS IN THE ATTACHMENT.]

f(x) =2x⁴  – 2x³  –7x²  + 3x  + 6

= (2x²-3)(x²-x-2)

= (2x²-3) (x-2) (x-1)

f(x)=0

= (2x²-3) =0 , (x-2)= 0 , (x-1)=0

x= √3/2, -√3/2, 2 ,-1

Hence , all the zeroes of the given Polynomial are: (√3/2), (-√3/2), -1,2

HOPE THIS WILL HELP YOU …..