If 2 + \sqrt{3} is a polynomial root, name another

SchachtN

SchachtN

Answered question

2021-08-18

If 2+3 is a polynomial root, name another root of the polynomial, and explain how you are certain it is also a root

Answer & Explanation

Laaibah Pitt

Laaibah Pitt

Skilled2021-08-19Added 98 answers

Step 1 
If 2+3 is a polynomial root, name another polynomial root
Step 2 
To find: the another root of the polynomial. 
Since 2+3 is an irrational number then the other root should be the conjugate of 2+3
Hence, the conjugate of 2+3 is 23 
23 is another root of the polynomial. 
It must be a root because we know that 

The roots of an equation are the solutions to the equation
λ1.2=b±b24ac2a 
Hence, the roots of an equation are conjugate to each other. 
23 is another root of the polynomial.

Jeffrey Jordon

Jeffrey Jordon

Expert2022-08-02Added 2605 answers

Answer is given below (on video)

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