write the polynomial of least degree with roots 4=5i and -1

Question

anonymous · Answer

help,anyone?.. im so confused :(

anonymous · Answer

* 4+5i and -1

anonymous · Answer

okay so we know that one root is $-1$... and we also know that another root is $4-5i$, but you need to remember that anytime you have a root that is in $a\pm bi$ form, it's conjugate is also a root.
eg. A polynomial has roots $-2$, $3$, and $1+5i$, write the polynomial of least degree:
so you would have $x=-2$, $x=3$, $x=1+5i$, but also $x=1\color{red}{-}5i$.
now to write it out, you would solve each one of the x's to make them equal to zero:$$x=-2~~~\implies~~~x+2=0$$$$x=3~~~\implies~~~x-3=0$$$$x=1+5i~~~\implies~~~x-1-5i=0$$$$x=1-5i~~~\implies~~~x-1+5i=0$$so now you have 4 binomials: $(x+2), (x-3), (x-1-5i), and (x-1+5i)$.
now to write the polynomial, simply multiply all the binomials together:$$(x+2)(x-3)(x-1-5i)(x-1+5i)$$ and the result would be your answer :)

now to solve your question, do the same steps :D

anonymous · Answer

@yummydum THANK YOU SO MUCH! :)

anonymous · Answer

No Problem, bro! :D