Question

find a quadratic polynomial whose zeros are under root 2 + 3 and under root 2 minus 3​

Answer 1

If $\alpha\:\:and\beta$ are zeroes, then it can be written as ,

$\large\green{\boxed{k[x^{2}-(\alpha+\beta)x+\alpha\beta]}}$

$\longrightarrow \alpha\beta= (3+\sqrt{2}) (\sqrt{2}-3) =2-3=-1$

$\longrightarrow \alpha+\beta=\sqrt{2}-3+\sqrt{2}+3=2\sqrt{2}$

Putting the values,

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

=$k[x^{2}-(2\sqrt{2})x+(-1) ]$

=${\underline{\boxed{\red{k[x^{2}-2\sqrt{2}x-1]}}}}$