Find the roots of the equation:

\[ x^2 + 10x + 34 = 0 \]

x 2 + 10 x + 34 = 0 x 2 + 2 \cdotx ⋅ 5 + 5 2 + 9 = 0 ( x + 5 ) 2 = − 9 ⇒ n o re a l so l u t i o n ( x + 5 ) 2 = 9 ⋅ i 2 ⇒ ( x + 5 = 3 i or x + 5 = − 3 i ) x 1 ​ = − 5 + 3 i , x 2 ​ = − 5 − 3 i → tw o co m pl e x n u mb ers so l u t i o n

Answered by kate200468 | 2024-06-10

x 2 + 10 x + 34 = 0 Δ = 1 0 2 − 4.1.34 = 100 − 136 = − 36 x = 2 − 10 ± − 36 ​ ​ = 2 − 10 ± 6 i ​ = − 5 ± 3 i ​

Answered by Ryan2 | 2024-06-10

The roots of the equation x 2 + 10 x + 34 = 0 are complex numbers, given by − 5 + 3 i and − 5 − 3 i . They are derived using the quadratic formula, which indicates the presence of complex solutions when the discriminant is negative. Thus, there are no real solutions for this quadratic equation.
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Answered by kate200468 | 2024-12-24