Question

Form a quadratic polynomial whose zeros are 3+√2 and 3−√2

Answer 1

Given:

$\text{ Roots of quadratic polynomial are }3+\sqrt{2}\text{ and }3-\sqrt{2}$

Required:

Find quadratic equation.

Explanation:

We can write it as

$\begin{gathered} =(x-(3+\sqrt{2}))(x+(-3+\sqrt{2})) \\ \text{ We can further write it as} \\ =(x-3-\sqrt{2})(x-3+\sqrt{2}) \\ =x^2-6x+7 \end{gathered}$

Answer:

$\text{ The given roots are roots of }x^2-6x+7$