Question

find the quadratic polynomial whose zeros are 3 + root 5 upon 2 and 3 minus root 5 upon 2​

Answer 1

sum if zeros

$\alpha + \beta = \frac{3 + \sqrt{5} }{2} + \frac{3 - \sqrt{5} }{2 } \\ \: \: \: \: \: \: \: \: \: = 3$

product of zeros

$\alpha \beta = \frac{3 + \sqrt{5} }{2} \times \frac{3 - \sqrt{5} }{2} \\ \: \: \: \: \: \: = \frac{9 - 5}{4} = 1$

polynomial is

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

$a( {x}^{2} - 3x + 1)$

where a is any real or complex number

Answer 2

Answer: 2x^2 - 3x +2

Step-by-step explan