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

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sapon | Student, Undergraduate | (Level 2) Honors

Posted March 16, 2011 at 7:55 AM via web

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Is it possible?

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

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted March 17, 2011 at 4:32 AM (Answer #2)

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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.

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted March 17, 2011 at 11:20 AM (Answer #3)

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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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