Sunday, March 31, 2013

Obtain all other zeroes of 3x4 + 6x3 – 2x2 – 10x – 5, if two of its zeroes are √(5/3) and - √(5/3)

Obtain all other zeroes of 3x4 + 6x3 – 2x2 – 10x – 5, if two of its zeroes are √(5/3) and  - √(5/3)


Quotient is
x2+2x+1  
Compare the equation with  ax2  + bx  + c  = 0
We get
a = 1 ,b=2 c= 1
To factorize the value we have to find two value which
sum is equal to b     = 2
product is       a*c   =1*1 = 1
 1 and 1 are required values which
sum is      1 + 1   = 2
product is  1 * 1   = 1
So we can write middle term  2x  = x  + x 
We get
x2 + x + x + 1 =0
x (x +1) +1(x +1) = 0
( x + 1)( x + 1)            = 0
x+1 = 0 , x+1 = 0
x= -1 , x= - 1
so our zeroes are   
 - 1  -1 , √(5/3) and  - √(5/3)

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