Write a unique polynomial in factored form with real coeff. that meets the given cond:

zeros: 0(multiplicity of 2), 3(multiplicity of 1), 2 + 3i (multiplicity of 1); leading coefficient of 1

Question

Write a unique polynomial in factored form with real coeff. that meets the given cond:

zeros: 0(multiplicity of 2), 3(multiplicity of 1), 2 + 3i (multiplicity of 1); leading coefficient of 1

anonymous · Answer

Is the answer f(x)=1(x^2)(x-3)(x^2+9)

anonymous · Answer

seems right to me, I don't know what leading coefficient means though

anonymous · Answer

oh means you just put a number in the front of the whole equation

anonymous · Answer

hmm, I don't think that the complex one is correct. $$x^2 + 9 = 0 \Rightarrow x = \pm i \cdot 3$$

anonymous · Answer

ohh really..

anonymous · Answer

would it be x^2-4x+13

anonymous · Answer

@Stiwan

anonymous · Answer

I figured it out, instead of (x² + 9) it should be (x² -4x + 13). (x²-4x+13) has the complex roots 2+3i and 2-3i

anonymous · Answer

This is how i got there: $$(x-z) \cdot (x-\overline{z}) = x^2 - (z+\overline{z})x + z\overline{z}$$Now with$$z + \overline{z} = 4, z\overline{z} = 13$$ the aforesaid follows

anonymous · Answer

hm, yeah that's correct. somehow I didn't see your responses, sry