Answer
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(Solution 1, Solution 2) = ((-1 + √3i)/2, (-1 - √3i)/2)
↓Steps Explained:↓
Solve the quadratic:
Set up the a, b, and c values:
a = 1, b = 1, c = 1
Quadratic Formula
| = | -b ± √b2 - 4ac |
| 2a |
Calculate -b
-b = -(1)
-b = -1
Calculate the discriminant Δ
Δ = b2 - 4ac:
Δ = 12 - 4 x 1 x 1
Δ = 1 - 4
Δ = -3 <--- Discriminant
Since Δ < 0, we expect two complex roots.
Take the square root of Δ
√Δ = √(-3)
Since the square root < 0, we have an irrational answer
-b + Δ:
Numerator 1 = -b + √Δ
Numerator 1 = -1 + √-3
-b - Δ:
Numerator 2 = -b - √Δ
Numerator 2 = -1 - √-3
Calculate 2a
Denominator = 2 * a
Denominator = 2 * 1
Denominator = 2
Find Solutions
| Solution 1 = | Numerator 1 |
| Denominator |
Solution 1 = (-1 + √-3)/2
Solution 2
(Solution 1, Solution 2) = ((-1 + √3i)/2, (-1 - √3i)/2)
Solution 2 = (-1 - √-3)/2
Final Answer
(Solution 1, Solution 2) = ((-1 + √3i)/2, (-1 - √3i)/2)Take the Quiz Switch to Chat Mode
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