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

 

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

 Nov 1, 2018

Best Answer 

 #1
avatar+4402 
+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
avatar+4402 
+2
Best Answer

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
avatar+189 
+1

thank you

skye25  Nov 1, 2018

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