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Find the quadratic polynomial whose zeros are underoot 2 and 2 underoot 2​

Answer»

Step-by-step EXPLANATION:

roots \: are \: \sqrt{2} \: and \: 2 \sqrt{2} \\ x = \sqrt{2} \\ = > x - \sqrt{2} = 0 \\ and \: x = 2 \sqrt{2} \\ = > x - 2 \sqrt{2} = 0 \\ \\ (x - \sqrt{2} )(x - 2 \sqrt{2} ) = 0 \\ = > x(x - 2 \sqrt{2} ) - \sqrt{2} (x - 2 \sqrt{2} ) = 0 \\ = > {x}^{2} - 2 \sqrt{2} x - \sqrt{2} x + (2 \sqrt{2 } \times \sqrt{2} ) = 0 \\ = > {x}^{2} - 2 \sqrt{2} x - \sqrt{2} x + (2 \times 2)= 0 \\ = > {x}^{2} - 2 \sqrt{2} x - \sqrt{2} x + 4 = 0 \\ = > {x}^{2} - 3 \sqrt{2} x + 4 = 0


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