SOLUTION: Hi, I know how to do it if it is like: x^3+x^2+x+2 but not in this way: Find the complex zeros of each polinomial function. Write f in factored form. f(x)= x^4+5x^2+4 Show

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Hi, I know how to do it if it is like: x^3+x^2+x+2 but not in this way: Find the complex zeros of each polinomial function. Write f in factored form. f(x)= x^4+5x^2+4 Show      Log On


   

Question 852772: Hi, I know how to do it if it is like: x^3+x^2+x+2 but not in this way:
Find the complex zeros of each polinomial function. Write f in factored form.
f(x)= x^4+5x^2+4
Show me the work please. Thanks
Found 2 solutions by josmiceli, ewatrrr:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+x%5E4+%2B+5x%5E2+%2B+4+
Make this substitution:
Let +z+=+x%5E2+
+z%5E2+%2B+5z+%2B+4+=+0+
Complete the square
+z%5E2+%2B+5z+%2B+%285%2F2%29%5E2+=+-4+%2B+%285%2F2%29%5E2+
+z%5E2+%2B+5z+%2B+25%2F4+=+-16%2F4+%2B+25%2F4+
+z%5E2+%2B+5z+%2B+25%2F4+=+9%2F4+
+%28+z+%2B+5%2F2+%29%5E2+=+%283%2F2%29%5E2+
Take the square root of both sides
+z+%2B+5%2F2+=+3%2F2+
+z+=+-1+
and also
+z+%2B+5%2F2+=+-3%2F2+
+z+=+-4+
----------------
By substitution:
+x%5E2+=+-1+
+x+=+i+
+x+=+-i+
and
+x%5E2+=+-4+
+x+=+2i+
+x+=+-2i+
--------------
+f%28x%29+=+%28+x+%2B+i+%29%2A%28+x+-+i+%29%2A%28+x+%2B+2i+%29%2A%28+x+-+2i+%29+

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

f(x)= x^4+5x^2+4    Factor

f(x)= (x^2 + 4)(x^2 + 1) = 0

        x^2 = -4,  x = 2i, -2i

        x^2 = -1,  x = i, -i