Determine the type and number of solutions of

\[ 7x^2 + 3x + 8 = 0 \]

7 x 2 + 3 x + 8 = 0 Δ = 3 2 − 4 ⋅ 7 ⋅ 8 = 9 − 224 = − 115 ⇒ n o re a l so l u t i o n tw o co m pl e x so l u t i o n s Δ = − 115 = 115 ⋅ i 2 ⇒ Δ ​ = 115 ​ i x 1 ​ = 2 a − b − Δ ​ ​ = 2 ⋅ 7 − 3 − 115 ​ i ​ = 14 − 3 − 115 i ​ ​ x 2 ​ = 2 a − b + Δ ​ ​ = 2 ⋅ 7 − 3 + 115 ​ i ​ = 14 − 3 + 115 ​ i ​

Answered by kate200468 | 2024-06-10

7 x 2 + 3 x + 8 = 0 a = 7 , b = 3 , c = 8 Δ = b 2 − 4 a c = 3 2 − 4 ⋅ 7 ⋅ 8 = 9 − 224 = − 215 A n s w er : Δ i s n e g a t i v e , t hi s g i v es tw o ima g ina ry so l u t i o n s

Answered by Lilith | 2024-06-24

The equation 7 x 2 + 3 x + 8 = 0 has a negative discriminant of − 215 , indicating there are no real solutions. Instead, it has two complex (imaginary) solutions. Therefore, the quadratic has two imaginary solutions.
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Answered by Lilith | 2024-09-05