Question 553408
a) What is another root to this equation?


If a+bi is one root, then the conjugate a-bi is another root


So 6 - 5i is another root

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b) What are the factors of the equation?


If p and q are roots, then x-p and x-q are factors



So if 6+5i and 6-5i are roots, then x-(6+5i) and x-(6-5i) are factors


They can be simplified to x-6-5i and x-6+5i


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c) What is the quadratic equation with the given root?



Multiply the factors to get 


(x-6-5i)(x-6+5i)


((x-6)-5i)((x-6)+5i)


(x-6)^2-(5i)^2 ... Note: I'm using the difference of squares formula here


(x-6)^2-25i^2


(x-6)^2-25(-1)


(x-6)^2+25


x^2-12x+36+25


x^2-12x+61



So the quadratic equation with the given root is x^2-12x+61 = 0


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d) What is the representative function? 


The function is f(x) = x^2-12x+61



All we're doing here is replacing the =0 part with f(x) = ...



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