Question

Find all the zeroes of the polynomial 3x⁴+6x³-2x²-10x-5 if two of its zeroes are (√5/3) and (-√5/3)
(class 10 CBSE SAMPLE PAPER 2017-18 MATHS)

Answer 1

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:


Given :


Two zeroes are (√5/3) & (-√5/3)


So, (x-√5/3) & (x+√5/3) are the factors of given Polynomial.


(x-√5/3)  (x+√5/3)


= x²- 5/3= (3x²-5)/3


= (3x²-5)/3=0


3x²-5 is a factor of given Polynomial


Divide 3x⁴+6x³-2x²-10x-5 by 3x²-5


[Division is in the attachment.]


Hence , all the zeroes of the given Polynomial are:

(√5/3), (-√5/3), -1,1



Hope this will help you...