Question

Find the quadratic polynomial whose zeros are 3 minus root 3 by 5 and 3 + root 3 by 5

Answer 1

$\alpha = \frac{3 - \sqrt{3} }{5} \\ \beta = \frac{3 + \sqrt{3} }{5} \\ \alpha + \beta = \frac{3 - \sqrt{3} }{5} + \frac{3 + \sqrt{3} }{5} \\ \alpha + \beta = \frac{6}{5} \\ \alpha \beta = ( \frac{3 - \sqrt{3} }{5} )( \frac{3 + \sqrt{3} }{5} ) \\ \alpha \beta = \frac{9 - 3}{25} = \frac{6}{25}$
from standard equation we know that
$a {x}^{2} + bx + c \\ {x}^{2} - ( \frac{ - b}{a} )x + \frac{c}{a} \\ \alpha + \beta = \frac{ - b}{a} = \frac{6}{5} \\ \alpha \beta = \frac{c}{a} = \frac{6}{25} \\ {x}^{2} - \frac{6}{5} x + \frac{6}{25} \\ 25 {x}^{2} - 30x + 6$
is the answer polynomial.

Answer 2

hope it helps you a lot