# Is it possible?Is it possible for a polynomial of the 5th degree to have 2 real roots and 3 complex roots?

justaguide | College Teacher | (Level 2) Distinguished Educator

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No polynomial can have an even number of complex roots as complex roots always occur in pairs of conjugate complex numbers. That is if one root is a + ib, there has to be another root of the form a - ib. Therefore a polynomial of degree 5 cannot have 3 complex roots.

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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No, it is not possible. Since imaginary roots always come in pairs, then if there are any imaginary roots, there will always be an even number of imaginary roots.

Also, a polynomial of odd degree has to have an odd number of real roots.

So, a polynomial that has the complex root x + iy, has also as root, the conjugate x - iy.

So, a polynomial of 5 degree could have 2 or 4 imaginary roots and 3 or 1 real roots.
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