Question

Find the quadratic equation whose one root is 1+√2 and the sum of its roots is 2
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Answer 1

Answer:

${x}^{2} - 2x - 1 = 0$

Step-by-step explanation:

$\alpha = 1 + \sqrt{2} \\ \\ \beta = 1 - \sqrt{2} \\ \\ s = 2 \\ \\ p = (1 + \sqrt{2} )(1 - \sqrt{2} ) \\ = 1 - 2 \\ = - 1 \\ \\ \\ {x}^{2} - sx + p = 0 \\ \\ {x }^{2} - 2x + ( - 1) = 0 \\ \\ {x}^{2} - 2x - 1 = 0$