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3. Obtain all other zeroes of

3x^4 + 6x^3 – 2x^2 – 10x – 5

, if two of its zeroes are

{√{5/3}}

and

{-√{5/3}}

Solution:
	Since   ${√{5/3}}$  and  ${-√{5/3}}$   are its zeroes,
	therefore  $(x- {√{5/3})(x+{√{5/3})$  are factor of the polynomial.
	i.e  $x^2-{5/3}$  or  $3x^2-5$  is factor of the polymial.

	Divide  $3x^4 + 6x^3 – 2x^2 – 10x – 5$  by  $3x^2-5$

3x^4 + 6x^3 – 2x^2 – 10x – 5

{3x^2-5}

x^2

+ 2x

+1

 ${3x^4}$       ${-5x^2}$

(

-

)

     ( $+$ )

6x^3 + 3x^2 -10x - 5

 ${6x^3 }$         ${-10x}$

(

-

)

       ( $+$ )

 ${3x^2}$      ${-5}$

 ${3x^2}$      ${-5}$

( $-$ )     ( $+$ )

Since the remainder is zero,

x^2+2x+1

is a factor of

3x^4 + 6x^3 – 2x^2 – 10x – 5

Factorised

x^2+2x+1

by splitting the middle term

Therefore   $x^2+2x+1$  =  $x^2+x+x+1$  
					  =  $x(x+1)+1(x+1)$ 
					  = $(x+1)(x+1)$ 
So zeores of the polynomial are  $-1$  and  $-1$

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Chapters For Class X- CBSE