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X^3+2x^2+3x+4=0 why the value of x is complex number?
Why are there no rational roots?
If a polynomial has a rational root, that root must be a divisor of the constant term divided by the leading coefficient. In this case, the constant term is 4 and the leading coefficient is 1, so the only possible rational roots are ±1, ±2, and ±4. However, if we plug any of those into the equation, we get a non-zero result, which means they are not roots. Therefore, there are no rational roots.