Question

solve: ix^2 - x + √2i = 0​

Answer 1

Answer:

The discriminant was positive so you expected two distinct roots. You didn’t expect imaginary roots though.

The difference is your assumptions only hold for polynomials with real coefficients.

This is a polynomial with some complex (non real) coefficients.

We can solve it using the quadratic equation:

x=−b±b2–4ac−−−−−−√2ax=−b±b2–4ac2a

x=−(−1)±(−1)2–4i(2i)−−−−−−−−−−√2ix=−(−1)±(−1)2–4i(2i)2i

x=1±1–8i2−−−−−√2ix=1±1–8i22i

x=1±9–√2ix=1±92i

x=i(1±3)−2x=i(1±3)−2

x = -2i or i

Notice the roots are not conjugate pairs either, which also is different to real coefficient polynomials.

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