Answer:
Correct answer: (x - 2 - 5 i) (x - 2 + 5 i)
Explanation:
Given:
x² - 4 x + 29 = ( ) ( ) = ?
this equation has no solution in the set of real numbers
x² - 4 x + 29 = x² - 2 · x · 2 + 2² - 2² + 29 = x² - 2 · x · 2 + 4 - 4 + 29
x² - 4 x + 29 = (x - 2)² + 25 = (x - 2)² - ( - 25) = (x - 2)² - ( - 1 · 5²)
We know that the imaginary unit is the equal i = √- 1 ⇒ i² = - 1
x² - 4 x + 29 = (x - 2)² - ( 5 i)² this is the difference of the square
x² - 4 x + 29 = (x - 2 - 5 i) (x - 2 + 5 i)
these are conjugated complex numbers
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