2-√5 2+√5from the quadratic equation from the roots given below? �

1.	2-√5 2+√5from the quadratic equation from the roots given below?
Answer» ANSWER: P(X) $= x^{2} - 4x - 1$ Step-by-step EXPLANATION: $\alpha = 2 - \sqrt{5}$ $\beta = 2 + \sqrt{5}$ $\alpha + \beta = 2 - \sqrt{5} + (2 + \sqrt{5}) = 4$ $\alpha \beta = (2 - \sqrt{5})(2 + \sqrt{5}) = (2)^{2} - (\sqrt{5} )^{2} = 4 - 5 = -1$ and we KNOW that the POLYNOMIAL is of the form :- $= x^{2} - (\alpha + \beta )x + \alpha \beta$ $= x^{2} - (4)x + (-1)$ $= x^{2} - 4x - 1$