In the given equation,, find all zeros of the given

Vikolers6

Vikolers6

Answered question

2021-12-15

In the given equation,, find all zeros of the given polynomial.
3x32x27x2

Answer & Explanation

otoplilp1

otoplilp1

Beginner2021-12-16Added 41 answers

Step 1
Given polynomial is 3x32x27x2
To find all zeros of the given polynomial.
Solution:
Finding zeroes of the given polynomial.
3x32x27x2=0
3x3+3x25x25x2x2=0
3x2(x+1)5(x+1)2(x+1)=0
(x+1)(3x25x2)=0
(x+1)(3x26x+x2)=0
(x+1)(3x(x-2)+1(x-2))=0
(x+1)(x-2)(3x+1)=0
(x+1)=0 or (x-2)=0 or (3x+1)=0
x=-1 or x=2 or x=13
Step 2
Hence, zeroes of the given polynomial are 13, -1 and 2.
Mary Goodson

Mary Goodson

Beginner2021-12-17Added 37 answers

Step 1
We have the given equation as
f(x)=3x32x27x2
On solving further by grouping the terms, we get the result as
f(x)=3x32x27x2
f(x)=3x3+4x26x2+x8x2
f(x)=x(3x2+4x+1)2(3x2+4x+1)
f(x)=(x2)(3x2+4x+1)
Step 2
On solving further by grouping the terms again, we get the result as
f(x)=(x2)(3x2+4x+1)
f(x)=(x2)(3x2+3x+x+1)
f(x)=(x-2)(3x(x+1)+1(x+1))
f(x)=(x-2)(x+1)(3x+1)
Now, zeros of the equation f(x)=3x22x27x2 is calculated as
f(x)=0
(x-2)(x+1)(3x+1)=0
x=2, -1, and 13
Hence, zeros of 3x32x27x2 are 2,-1, and 13.

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