Thread: Find All Zeros (real and imaginary)

I need to use the given zero to find all the zeros real or imaginary of the function and also write f as a product of linear factors.

Zero: 5-i

F(x)=(3x^6)-(43x^5)+(218x^4)-(428x^3)+(156x^2)+300x-104

Originally Posted by Kairo

I need to use the given zero to find all the zeros real or imaginary of the function and also write f as a product of linear factors.

Zero: 5-i

F(x)={3x^6}-{43x^5}+{218x^4}-{428x^3}+{156x^2}+300x-104

If is a root of , then also a root. Thus and are factors of . Divide by , and then you will get the quadric By plugging in possible integer roots, find that yields the quadric zero, so is a factor of it. Divide the quadric by , and you will get . Keep going like this and find the roots of the cubic. Writing the equation as the product of linear factors means writing [LaTeX ERROR: Convert failed] as , where , , , , , and are the roots you were asked to find, of which we already have three: , , and , and the other three are the roots of the cubic .