Question

find the quadratic polynomial whose zeroes are root 3+root5 and root5-root3​

Answer 1

Step-by-step explanation:

roots are

$\frac{ 3 + \sqrt{5} }{5} \: \: \: \: and \: \: \: \: \frac{3 - \sqrt{5} }{5}$

product of roots are

$(\frac{3 + \sqrt{5} }{5} )( \frac{3 - \sqrt{5} }{5} ) \\ = \frac{9 - 5}{25} \\ = \frac{4}{25}$

sum of the roots are

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

quadratic equation is given by

${x}^{2} - (sum \: of \: roota ) + (product \: of \: roots) = 0$

${x}^{2} - \frac{3}{5} x + \frac{4}{25} = 0$

${25x}^{2} - 15x + 4 = 0$

${\red {hope \: you \: \ like \: it}}$