SchachtN

2021-08-18

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

Laaibah Pitt

Skilled2021-08-19Added 98 answers

Step 1

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

Step 2

To find: the another root of the polynomial.

Since $2+\sqrt{3}$ is an irrational number then the other root should be the conjugate of $2+\sqrt{3}$.

Hence, the conjugate of $2+\sqrt{3}$ is $2-\sqrt{3}$

$\therefore 2-\sqrt{3}$ 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

$\lambda 1.2=\frac{b\pm \sqrt{{b}^{2}}-4ac}{2a}$

Hence, the roots of an equation are conjugate to each other.

$\therefore 2-\sqrt{3}$ is another root of the polynomial.

Jeffrey Jordon

Expert2022-08-02Added 2605 answers

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