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