Question

if one zero of the polynomial is 3-√5 and product of zero is 4. form a quadratic equation​

Answer 1

Step-by-step explanation:

$\Huge\underline{\underline{\sf ANSWER}}\\ Let \: \alpha \: be \: one \: zero = 3 - \sqrt{5} \\ product \: = 4 \\ \alpha \times \beta = 4 \\ \beta = \frac{4}{3 - \sqrt{5} } \\ \\ \alpha + \beta \\ \frac{4}{3 - \sqrt{5} } + 3 - \sqrt{5} \\ \frac{4 + {(3 - \sqrt{5}) }^{2} }{3 - \sqrt{5} } \\ \frac{4 + 9 + 5 - 6 \sqrt{5} }{3 - \sqrt{5} } \\ \frac{18 - 6 \sqrt{5} }{3 - \sqrt{5} } \\ \\ {x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0 \\ {x}^{2} - ( \frac{18 - 6 \sqrt{5} }{3 - \sqrt{5} } )x + 4 = 0$