Question

Find a quadratic polynomial with zeros 3+â2 and 3-â2

Answer 1

Hello

Given that
$\alpha = 3 + {a}^{2} \\ \beta = 3 - {a}^{2}$
Now
The relation between the coefficients and Zeroes of the polynomial are

$\alpha + \beta = 3 + {a}^{2} + 3 - {a}^{2} \\ \alpha + \beta = 6 \\ \\ \alpha \beta = (3 + {a}^{2} )(3 - {a}^{2} ) \\ \alpha \beta = {3}^{2} - {a}^{4} = 9 - {a}^{4}$
Now,

The polynomial is of the form

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

So, the polynomial is
$k( {a}^{2} - 6a + 9 - {a}^{4} )$
When k is 1

Hope this will be helping you ✌️