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Question

Obtain all other zeroes of 3x4+6x32x210x5, if two of its zeroes are 53 and 53.

Solution
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Two zeroes are 53 and 53

So we can write it as, x = 53 and x = 53

we get x53=0 and x+53=0

Multiply both the factors we get,
x253=0

Multiply by 3 we get
3x25=0 is the factor of 3x4+6x32x210x5

Now divide, 3x4+6x32x210x5 by 3x25=0 we get,
Quotient is x2+2x+1=0

Compare the equation with quadratic formula,
x2(Sum of root)x+(Product of root)=0

Sum of root =2
Product of the root =1

So, we get
x2+x+x+1=0

x(x+1)+1(x+1)=0

x+1=0,x+1=0

x=1,x=1

So, our zeroes are 1,1, 53 and 53

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