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Suppose a polynomial of degree 4 with rational coefficients has the given numbers as zeros. Find the other zero

-2, square root 5, 10/3

Suppose a polynomial of degree 4 with rational coefficients has the given numbers-example-1
User Cristiana Chavez
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1 Answer

13 votes
13 votes

Explanation:

The root is

-sqr root of 5.

First, we put these roots in the forn of


(x - a)

where a is the root

So we have


(x - ( - 2))(x - √(5) )(x - (10)/(3) )


(x + 2)(x - √(5) )(3x - 10)


(3 {x}^(2) - 4x - 20)(x - √(5) )

To get rid of that square root, let have another root that js the conjugate posive root of 5.


(3 {x}^(2) - 4x - 20)(x - √(5) )(x + √(5) )


(3 {x}^(2) - 4x - 20)(x {}^(2) + 5)

Which will gives us a rational coeffeicent of degree 4.

Why we didn't do


(x - √(5) )

?

Because


(x - √(5) ) {}^(2) = {x}^(2) - 2 √(5) + 5

If we foiled out we will still have a irrational coeffceint.

User Neoneye
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