Question

Find a polynomial function with real coefficients that has the given zeros
1 -√3i, 2

Answer 1

`x^3-4x^2+8x-8`

Explanation:

`\displaystyle\\(x-(1-√(3) i)(x-(1+√(3) i)(x-2)=\\\\(x^2-(1-√(3) i)x-(1+√(3) i)x+(1-√(3) i)(1+√(3) i))(x-2)=\\\\(x^2-x+√(3) i-x-√(3) i+1-(√(3) i)^2)(x-2)=\\\\(x^2-2x-3\cdot(-1))(x-2)=\\\\(x^2-2x+4)(x-2)=\\\\x^3-2x^2+4x-2x^2+4x-8=\\\\x^3-4x^2+8x-8`