Write a quadratic equation in the variable x with the solutions sqrt{2} and -sqrt{8}.

Question

Write a quadratic equation in the variable x with the solutions sqrt{2} and -sqrt{8}.

Answer 1

0 = (x - √2)(x - (-√8))

 

   = (x - √2)(x + √8) = x² - (√2)x + (√8)x - 4

 

                                = x² - (√2)x + (2√2)x - 4

 

                               0 = x² + (√2)x - 4

Answer 2

A(x - √2)(x + √8) = 0

 

where A is any real number ≠ 0.  You can expand it to the standard form

 

ax² + bx + c = 0 

 

if you wish.