Find a third-degree polynomial equation with rational coefficients that has roots –4 and 2 + i
1 answer:
If it has rational coefients and is a polygon
if a+bi is a root then a-bi is also a root
the roots are -4 and 2+i
so then 2-i must also be a root
if the rots of a poly are r1 and r2 then the factors are
f(x)=(x-r1)(x-r2)
roots are -4 and 2+i and 2-i
f(x)=(x-(-4))(x-(2+i))(x-(2-i))
f(x)=(x+4)(x-2-i)(x-2+i)
expand
f(x)=x³-11x+20
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