Question

5. Find a quadratic polynomial if sum and product of its zeroes are √2 and 1/2 respectively

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Answer 1

Now formula of quadratic equation is x²-(Sum of root)x + (Product of root) = 0 Plug the value in formula we get x² –(√2)x  + 1/2  = 0  Multiply by 2 to remove denominator we get 3x²  - 2√2 x +1=0

Answer 2

Here is your solution :-

Given,

$sum \: of \: roots \: ( \alpha + \beta ) = \sqrt{2} \\ \\ product \: of \: roots( \alpha \beta ) = \frac{1}{2} \\ \\ eqution \: of \: polynomial \: = \\ \\ {x}^{2} - ( \alpha + \beta )x + ( \alpha \beta ) = 0 \\ \\ {x}^{2} - \sqrt{2} x + \frac{1}{2 } = 0 \\ \\ multiply \: by \: 2 \\ \\ 2 {x}^{2} - 2 \sqrt{2} x + 1 = 0$

Hope it helps.