Question

Form the quadratic equation from the roots given below.

\[2 - \sqrt{5}, 2 + \sqrt{5}\]

Answer 1

\[2 - \sqrt{5}, 2 + \sqrt{5}\] 

Sum of roots = \[2 - \sqrt{5} + 2 + \sqrt{5} = 4\]

Product of roots = \[\left( 2 - \sqrt{5} \right)\left( 2 + \sqrt{5} \right)\]

= 4 - 5

= -1 

The general form of the quadratic equation is x² - Sum of roots x + Product of roots = 0 

So, the quadratic equation obtained is

x² - 4x +  (-1) = 0 

x² - 4x - 1 = 0