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

Asked on by sapon

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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.

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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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