Question

Find the quadratic polynomial whose zeros are 5 + √2 and 5 -√2 .

Answer 1

Answer:

$let \: 5 + \sqrt{2} = a \\ 5 - \sqrt{2} = b \\ a + b = 5 + \sqrt{2} + 5 - \sqrt{2} \\ = 10 \\ a \times b \: = (5 + \sqrt{2} ) \times (5 - \sqrt{2} ) \\ = {5}^{2} - { \sqrt{2} }^{2} = 25 -2 = 23 \\ required \: polynmial \: = {x}^{2} - (a + b)x </p><p>+ a \times b \\ = {x}^{2} - 10x + 23$