Enter the polynomial

Question

Form a polynomial f(x) with real coefficients having the given degree and zeros.
Degree 4; zeros: 6, multiplicity 2; 3i

Answer 1

Since f(x) has real coefficients and 3i is a zero, then -3i is also a zero.  

 

Since f(x) has degree 4, there can't be more than 4 distinct zeros.  

 

The roots are 3i, -3i, 6(with multiplicity 2)

 

f(x) = (x-6)(x-6)(x-3i)(x-(-3i))

 

      = (x²-12x+36)(x²+9)

 

      = x⁴+9x²-12x³-108x+36x²+324 = x⁴-12x³+45x²-108x+324

 

Answer 2

Hi Jessica,

 

Degree 4 so there are four roots. multiplicity 2 means the term is squared. Complex roots come in conjugate pairs so the other complex root must be -3i.

 

f(x) = (x - 6)²(x - 3i)(x + 3i)