Polynomials, SMB-011 `g(x)=(x-1)(x^2-2x+8)`. Justify that `g(x)` only has one zero. (2 marks) --- 5 WORK AREA LINES (style=lined) --- Show Answers Only `text{Proof (See worked solutions)}` Show Worked Solution `g(x)=(x-1)(x^2-2x+8)`. `g(1)=0\ \ =>\ \ text{one zero at}\ \ x=1` `text{Consider the roots of}\ \ y=x^2-2x+8` `Δ = b^2-4ac=(-2)^2-4*1*8=-28<0` `text{Since}\ \ Δ<0\ \ =>\ \ text{No zeros (roots)}` `:. g(x)\ text{only has 1 zero}`