write a polynomail function of least degree with rational coefficients so that P(x)=0 has roots 3i,3-i?

Answers

Answer #1 | 13/02 2014 07:21

If an equation P(x) = 0 with real coefficients, has a complex solution (a+bi), then has also its conjugate (a-bi)
If P(x) has roots 3i and 3 - i, then it must have also
-3i and 3 + i
remember that if a is a root then the polynomial contains the factor (x - a)
the minimal degree polynomial is then
P(x) = (x - 3i)(x + 3i)(x - (3 - i))(x - (3 + i))
P(x) = x^4 - 6 x^3 + 19 x^2 - 54 x + 90

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Answer #1| 13/02 2014 07:2124 %