Find a quadratic equation with the roots of $r _ { 1 } = 1 - \sqrt { 2 } \text { and } r _ { 2 } = 1 + \sqrt { 2 }$ . Write the answer in the form $$a x ^ { 2 } + b x + c = 0$$ where a, b, and c are integers and $a = 1$ . A) x² + 4x + 1 = 0 B) x² - x-1 = 0 C) x² - 2x-1 = 0 D) x² + x-2 = 0 E) x² + 2x -1 = 0

Question

Quizplus · Accepted Answer

The sum of the roots $ (1 - \sqrt{2}) + (1 + \sqrt{2}) = 2 $ and the product of the roots $ (1 - \sqrt{2})(1 + \sqrt{2}) = 1 - 2 = -1 $. The quadratic equation is $ x^2 - (sum)x + (product) = 0 $, which simplifies to $ x^2 - 2x - 1 = 0 $.

Find a Quadratic Equation with the Roots Of r1=1−2 and r2=1+2r _ { 1 } = 1 - \sqrt { 2 } \text { and } r _ { 2 } = 1 + \sqrt { 2 }r1​=1−2​ and r2​=1+2​

Find a Quadratic Equation with the Roots Of $r _ { 1 } = 1 - \sqrt { 2 } \text { and } r _ { 2 } = 1 + \sqrt { 2 }$