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(A) The general form of a quadratic equation is $x^{2} - (	ext{sum of roots})x + (	ext{product of roots}) = 0$.Given roots are $\alpha = \sqrt{2}$ a

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$x^{2}-3 \sqrt{2} x+4=0$

Vedclass · Answer

(A) The general form of a quadratic equation is $x^{2} - (	ext{sum of roots})x + (	ext{product of roots}) = 0$.Given roots are $\alpha = \sqrt{2}$ and $\beta = 2\sqrt{2}$.Sum of roots $= \alpha + \beta = \sqrt{2} + 2\sqrt{2} = 3\sqrt{2}$.Product of roots $= \alpha \cdot \beta = (\sqrt{2}) \cdot (2\sqrt{2}) = 2 \cdot 2 = 4$.Substituting these values into the general form,we get:$x^{2} - (3\sqrt{2})x + 4 = 0$.

Construct a quadratic equation whose roots are $\sqrt{2}$ and $2 \sqrt{2}$.

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