Question

find
quadratic
Polynomial where zerws are 3+√5 by 5
of 3-root5 by 5​

Answer 1

Step-by-step explanation:

alpha beta are roots of equation

Answer 2

Step-by-step explanation:

Let ,

$\alpha \: be \: \frac{3 + \sqrt{5} }{5}$

$and$

$\beta \: be \: \frac{3 - \sqrt{5} }{5}$

We know formula of quadratic ,

${x}^{2} - ( \alpha + \beta )x \: + ( \alpha \beta ) = 0$

So let's find,

$\alpha + \beta \\ and \\ \alpha \beta$

$\alpha + \beta = \frac{3 + \sqrt{5} }{5} + \frac{3 - \sqrt{5} }{5}$

$therefore \\ \alpha + \beta = \frac{6}{5}$

$now \\ \alpha \beta = \frac{3 + \sqrt{5} }{5} \times \frac{3 - \sqrt{5} }{5}$

$\alpha \beta = \frac{4}{25}$

$ok \: we \: have \: almost \: done \\ now \: lets \: finish \: this \: problem$

$so \: this \: is \: your \: required \: answer$

${x}^{2} - \frac{6}{5}x \: + \frac{4}{25} = 0$

Hope it helps uh!