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A polynomial equation with rational coefficients has roots +5 plus 12 i and −−negative 9 minus 7 i. List two more roots of the equation.

Sagot :

MrRoyal

Answer:

The additional roots are: [tex]5 - 12i[/tex] and [tex]-9 + 7i[/tex]

Step-by-step explanation:

Given

Roots: [tex]5 + 12i[/tex] and [tex]-9 -7i[/tex]

Required

Determine two additional roots

For a polynomial with two rational roots, the additional roots are the conjugates of the roots.

Take for instance, the following expression:

[tex]a + \sqrt b[/tex]

The conjugate of [tex]a + \sqrt b[/tex] is: [tex]a - \sqrt b[/tex].

Having established how to determine the additional roots, we proceed to determine the roots.

The conjugate of [tex]5 + 12i[/tex] is [tex]5 - 12i[/tex] and the conjugate of [tex]-9 -7i[/tex] is [tex]-9 + 7i[/tex]

Hence, the additional roots are: [tex]5 - 12i[/tex] and [tex]-9 + 7i[/tex]

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