Question

Obtain all other zeroes of 3x4 + 6x3 – 2x2 – 10x – 5, if two of its zeroes are √(5/3) and-√(5/3).
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Answer 1

Step-by-step explanation:

Two zeroes are 35 and −35

So we can write it as, x = 35 and x = −35

we get x−35=0 and x+35=0

Multiply both the factors we get,

x2−35=0

Multiply by 3 we get

3x2−5=0 is the factor of 3x4+6x3−2x2−10x−5

Now divide, 3x4+6x3−2x2−10x−5 by 3x2−5=0 we get,

Quotient is x2+2x+1=0

Compare the equation with quadratic formula,

x2−(Sum  of  r−(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, 35 and −35