+0

# complex zeros for the polynomial function

0
355
2
+202

f(x)=x^4+5x^2+6

Enter the number of complex zeros for the polynomial function in the box.

Nov 1, 2018

#1
+5770
+2

In general the number of complex zeros will be equal to the degree of the polynomical.

But it's possible that some of these zeros are repeated.

f(x) here is just a quadratic in x2 so we may be able to easily factor it

$$f(x)=x^4+5x^2+6 = \\ (x^2+3)(x^2+2) =\\ (x+i\sqrt{3})(x-i\sqrt{3})(x+i\sqrt{2})(x-i\sqrt{2})\\ \text{and you can see that we have 4 distinct complex roots}$$

.
Nov 1, 2018

#1
+5770
+2

In general the number of complex zeros will be equal to the degree of the polynomical.

But it's possible that some of these zeros are repeated.

f(x) here is just a quadratic in x2 so we may be able to easily factor it

$$f(x)=x^4+5x^2+6 = \\ (x^2+3)(x^2+2) =\\ (x+i\sqrt{3})(x-i\sqrt{3})(x+i\sqrt{2})(x-i\sqrt{2})\\ \text{and you can see that we have 4 distinct complex roots}$$

Rom Nov 1, 2018
#2
+202
+1

thank you

skye25  Nov 1, 2018