Question

Find the quadratic polynomial where zeros are 2+root3 and 2-root3

Answer 1

Answer:

$sum = (2 + \sqrt{3} ) + (2 - \sqrt{3}) \\ \\ = 4 \\ \\ product = (2 + \sqrt{3} )(2 - \sqrt{3} ) \\ \\ = 4 - 2 \sqrt{3} + 2 \sqrt{3} - 3 \\ \\ = 4 - 3 = 1 \\ \\ {x}^{2} - (sum)x + (product) \\ \\ {x}^{2} - 4x + 1$