Question

Find all zeros of the polynomial $f(x)= 2x^{4} -2x^{3}-7x^{2}+3x+6$ if its two zeros are $-\sqrt \frac{3} {2} and \sqrt \frac{3} {2}$

Answer 1

Method of finding the remaining zeros of a polynomial when some 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 : Two Zeroes of the polynomial are - √3/2 & √3/2. Therefore ,    

(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)

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

[DIVISION IS IN THE ATTACHMENT.]

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

HOPE THIS ANSWER WILL HELP YOU …..

Answer 2

Answer:

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