Question

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes

respectively:-1/√2 ,1/√2​

Answer 1

Answer:

$let \\ \alpha = \frac{ - 1}{ \sqrt{2} } \: \: \: \beta = \frac{1}{ \sqrt{2} } \\ \alpha + \beta = \frac{ - 1}{ \sqrt{2} } + \frac{1}{ \sqrt{2} } = \frac{0}{ \sqrt{2} } = 0 \\ \alpha \beta = ( \frac{ - 1}{ \sqrt{2} } ) \times ( \frac{1}{ \sqrt{2} } ) = \frac{ - 1}{2} \\ required \: quadratic \: equation \\ {x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0 \\ {x}^{2} - (0 )x + (\frac{ - 1}{2} ) = 0 \\ {x }^{2} - \frac{ 1}{2} = 0 \\ multiply \: by \: 2 \: on \: both \: side \\ 2( {x}^{2} - \frac{1}{2} ) = 2 \times 0 \\ 2 {x}^{2} - 1 = 0$

This is your quadratic polynomial

& thanks for the question ❤️❣️(-:✌️✔️✍️