Question

2-√5 2+√5

from the quadratic equation from the roots given below? ​

Answer 1

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 :-

$= x^{2} - (\alpha + \beta )x + \alpha \beta$

$= x^{2} - (4)x + (-1)$

$= x^{2} - 4x - 1$