1 answer:
<span>In polynomials we have not of an imaginary unit (i), therefore we have the fourth zeros -1-2i.</span>
![f(x)=(x-5)(x+3)\left[x-(-1-2i)\right]\left[x-(-1+2i)\right]\\\\=(x^2+3x-5x-15)[x^2-x(-1+2i)-x(-1-2i)+(-1)^2-(2i)^2]\\\\=(x^2-2x-15)(x^2+x-2i+x+2i+1+4)\\\\=(x^2-2x-15)(x^2+2x+5)\\\\=x^4+2x^3+5x^2-2x^3-4x^2-10x-15x^2-30x-75\\\\=x^4-14x^2-40x-75](https://tex.z-dn.net/?f=f%28x%29%3D%28x-5%29%28x%2B3%29%5Cleft%5Bx-%28-1-2i%29%5Cright%5D%5Cleft%5Bx-%28-1%2B2i%29%5Cright%5D%5C%5C%5C%5C%3D%28x%5E2%2B3x-5x-15%29%5Bx%5E2-x%28-1%2B2i%29-x%28-1-2i%29%2B%28-1%29%5E2-%282i%29%5E2%5D%5C%5C%5C%5C%3D%28x%5E2-2x-15%29%28x%5E2%2Bx-2i%2Bx%2B2i%2B1%2B4%29%5C%5C%5C%5C%3D%28x%5E2-2x-15%29%28x%5E2%2B2x%2B5%29%5C%5C%5C%5C%3Dx%5E4%2B2x%5E3%2B5x%5E2-2x%5E3-4x%5E2-10x-15x%5E2-30x-75%5C%5C%5C%5C%3Dx%5E4-14x%5E2-40x-75)
Answer:
B)
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