Solve 2x² + 4x + 5 = 0
This quadratic does not have real roots because its discriminant is negative, so the quadratic formula gives a complex-conjugate pair.
Problem2x² + 4x + 5 = 0
Show detailed solution
Answer: x = −1 ± (√6/2)i
Step 1: identify a, b, and c
For 2x² + 4x + 5 = 0, the coefficients are a = 2, b = 4, and c = 5.
Step 2: calculate the discriminant
D = b² − 4ac = 4² − 4(2)(5) = 16 − 40 = −24. Because D is negative, the solutions are complex.
Step 3: apply the quadratic formula
x = (−4 ± √−24) ÷ 4. Since √−24 = 2√6 i, this becomes x = −1 ± (√6/2)i.
Step 4: decimal form
√6/2 ≈ 1.224744871, so the roots are approximately x = −1 ± 1.224744871i.