Find the zeros (if any) of the function y=x^{4}+3x^{2}+2 algebraically.

Ben Shaver

Ben Shaver

Answered question

2021-12-11

Find the zeros (if any) of the function y=x4+3x2+2 algebraically.

Answer & Explanation

Ronnie Schechter

Ronnie Schechter

Beginner2021-12-12Added 27 answers

Step 1
Given equation is y=x4+3x2+2.
Step 2
In order to find the zeroes of given equation putting y=0, then the solution of the equation will give the zeroes.
Step 3
The given equation can be solved algebraically by firstly making factors of the expression and then equating each factor to zero as shown below:
x4+3x2+2=0
x4+x2+2x2+2=0
x2(x2+1)+2(x2+1)=0
(x2+1)(x2+2)=0
Step 4
Equating each factor to zero, it gives
(x2+1)(x2+2)=0
x2+1=0
x=±i
and x2+2=0
x=±i2
Step 5
Thus, the given function has four imaginary zeroes only which are:
x=i,i,i2,i2
hysgubwyri3

hysgubwyri3

Beginner2021-12-13Added 43 answers

(x22)(x+1)(x1)=0
x22=0
x+1=0
x1=0
x=2,2
x=1
x=1
The final solution is all the values that make (x22)(x+1)(x1)=0 true.
x=2,2,1,1
The result can be shown in multiple forms.
Exact Form: x=2,2,1,1
Decimal Form:
x=1.41421356,1.41421356,1,1

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