A quadratic equation whose one root 1+√2 and sum of its root is 2, is

Dear student,Let the roots be α and βα=1+2α +β=2    (given)β=2-α=2-1-2β=1-2α β=1+21-2=-1quadratic equation will be given byx2-α +βx+α β=0x2-2x-1=0Regards

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here we have to find the quadratic equation whose one root is 1+ √2 and the sum of its roots is 2. let the other root of the equation be x. ➡ 1 + √2 + x = 2 ➡ x = 2 - 1 - √2 ➡ x = 1 - √2 another root of the quadratic equation is 1 - √2 therefore product of the roots = (1 + √2)(1 - √2) using identity (a + b)(a - b) = a² - b² = (1)² - (√2)² = 1 - 2 = -1 now we know that, sum of roots = -b/a product of roots = c/a 2 = -b/a ➡ b/a = -2 -1 = c/a therefore a = 1, b = -2 and c = -1 standard form of quadratic equation = ax² + bx + c hence, the quadratic equation is = x² - 2x - c
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