Question

Find a quadratic equation whose roots are 3- id="TexFormula1" title="\sqrt{3} and 3 +\sqrt{3}" alt="\sqrt{3} and 3 +\sqrt{3}" align="absmiddle" class="latex-formula">

Answer 1

Answer:

x² - 6x + 6 = 0

Step-by-step explanation:

Given the roots are x = 3 - $\sqrt{3}$ and x = 3 + $\sqrt{3}$ , then the corresponding factors are

(x - (3 - $\sqrt{3}$ ) ) and (x - (3 + $\sqrt{3}$ ) ), that is

(x - 3 + $\sqrt{3}$ ) and (x - 3 - $\sqrt{3}$ )

The equation is then the product of the factors

(x - 3 + $\sqrt{3}$ )(x - 3 - $\sqrt{3}$ ) = 0

(x - 3)² - ($\sqrt{3}$ )² = 0

x² - 6x + 9 - 3 = 0

x² - 6x + 6 = 0