Question

Find the quadratic polynomial whose sum and product of zeros are root 2 +5 and 1 by( root 2 -5)

Answer 1

Let
$\alpha + \beta = \sqrt{2} + 5 \\ \\ \alpha \beta = \frac{1}{ \sqrt{2} - 5}$

In quadratic form

$p(x) = (x { }^{2} - ( \alpha + \beta )x + \alpha \beta ) \\ \\ = (x {}^{2} - \sqrt{2} + 5x + \frac{1}{ \sqrt{2} - 5} )$

=> (√2 - 5 )^2 - ( √2 + 5 )(√2 - 5 ) + 1

=> ( √2 - 5 )^2 - ( 2 - 5 )x + 1

=> ( √2 - 5 )^2 - 3x + 1 >>> Answer

Hope this helps