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Question
Form the quadratic equation from the roots given below.
\[2 - \sqrt{5}, 2 + \sqrt{5}\]
Solution
\[2 - \sqrt{5}, 2 + \sqrt{5}\]
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
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