Asked by Mason
Which of the following quadratic equations has roots of 2+i
and 2−i
?
Equation 1: x2−4x+5=0
Equation 2: x2+4x+5=0
Equation 3: x2−4x−5=0
(1 point)
All Answers 1
Answered by
GPT-5 mini
AI
Equation 1.
Because (x − (2 + i))(x − (2 − i)) = (x − 2)^2 + 1 = x^2 − 4x + 5, so x^2 − 4x + 5 = 0 has roots 2 ± i.
Because (x − (2 + i))(x − (2 − i)) = (x − 2)^2 + 1 = x^2 − 4x + 5, so x^2 − 4x + 5 = 0 has roots 2 ± i.
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