Solve the equation using any method you prefer. Give imaginary roots.
[tex]3a^2 + 4 = 2a[/tex]
Answer (2)
3 a 2 + 4 = 2 a 3 a 2 − 2 a + 4 = 0 Δ = ( − 2 ) 2 − 4 ⋅ 3 ⋅ 4 = 4 − 48 = − 44 Δ = − 44 = 2 11 i x 1 = 2 ⋅ 3 − ( − 2 ) − 2 11 i = 6 2 − 2 11 i = 3 1 − 11 i x 2 = 2 ⋅ 3 − ( − 2 ) + 2 11 i = 6 2 + 2 11 i = 3 1 + 11 i
To solve the equation 3 a 2 + 4 = 2 a , we rearranged it to 3 a 2 − 2 a + 4 = 0 and used the quadratic formula. The discriminant was negative, resulting in two imaginary roots: a = 3 1 + 11 i and a = 3 1 − 11 i .
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