Question

Which equation has the solutions x=1 +/- square root of five

Answer 1

x² - 2x - 4 = 0

Explanation:

x = 1 + √5 or x = 1 - √5

sum of the root = (1 + √5) + (1 -√5)

sum of the root = 2

product of the root = (1 +√5)(1-√5)

product of the root = 1 +√5 -√5 -5

product of the root = 1 - 5

product of the root = -4

A quadratic equation is expressed by ;

x² -( sum of the root) + (product of the root )= 0

therefore,

x² - 2 - 4 = 0