Question

Find the Quadratic polynomial whose sum and product are root 2+1 and 1/root 2+1​

Answer 1

$\huge{\underline{\mathtt{\red{Ꭺ}\red{ղ}\green{Տ}\blue{ω}\purple{Ꭼ}\orange{я᭄}}}}$

General quadratic polynomial equation is:-

$\begin{gathered} {x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0 \\ \\ {x}^{2} - ( \sqrt{2} + 1)x + \frac{1}{ \sqrt{2} + 1 } = 0 \\ \\ {x}^{2} - ( \sqrt{2} + 1)x + \frac{1}{ \sqrt{2} + 1 } \times \frac{ \sqrt{2} - 1 }{ \sqrt{2} - 1} = 0 \\ \\\purple{\boxed{\pink{ {x}^{2} - ( \sqrt{2} + 1)x + ({ \sqrt{2} - 1 } ) = 0}}}\end{gathered}$

Answer 2

$\huge{\underline{\mathtt{\red{A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}$

❥ General quadratic polynomial ⠀⠀⠀⠀⠀⠀⠀equation is:-

$\begin{gathered}\begin{gathered} {x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0 \\ \\ {x}^{2} - ( \sqrt{2} + 1)x + \frac{1}{ \sqrt{2} + 1 } = 0 \\ \\ {x}^{2} - ( \sqrt{2} + 1)x + \frac{1}{ \sqrt{2} + 1 } \times \frac{ \sqrt{2} - 1 }{ \sqrt{2} - 1} = 0 \\ \\\pink{\boxed{\red{ {x}^{2} - ( \sqrt{2} + 1)x + ({ \sqrt{2} - 1 } ) = 0}}}\end{gathered}\end{gathered}$