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If `a ,b ,c` are nonzero real numbers and `a z^2+b z+c+i=0` has purely imaginary roots, then prove that `a=b^2c`

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To prove that \( a = b^2c \) given that the equation \( az^2 + bz + c + i = 0 \) has purely imaginary roots, we can follow these steps: ### Step-by-Step Solution: 1. **Assume a Purely Imaginary Root**: Let \( z = i\alpha \), where \( \alpha \) is a real number. This assumption is based on the fact that the roots are purely imaginary. 2. **Substitute the Root into the Equation**: ...
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