Question

Find the polynomial whose zeros are 3 root 5 and 3-root 5

Answer 1

Answer:

$\alpha + \beta = 3 \sqrt{5} - 3 \sqrt{5 } \\ = 0 \\ \\ \alpha \times \beta = 3 \sqrt{5} \times - 3 \sqrt{5 } \\ = - 45 \\ \\ polyn omial = k( {x}^{2} - (\alpha + \beta )x + \alpha \times \beta ) \\ = k( {x}^{2} - (0)x + ( - 45)) \\ = k( {x}^{2} - 45) \: \: (where \: k \: is \: not \: equal \: to \: zero)$