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

Question

Ronnie Schechter · Accepted Answer

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 · Accepted Answer

(x2−2)(x+1)(x−1)=0  x2−2=0  x+1=0  x−1=0  x=2,−2  x=−1  x=1  The final solution is all the values that make (x2−2)(x+1)(x−1)=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

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

Answered question

Answer & Explanation

New Questions in Algebra I