Question

How do you write a polynomial with roots of –1, –2, and 3?

Answer 1

`f(x)=x^3-7x-6`

Explanation:

`"Given a polynomial with roots, say"`

`x=a,x=b" and "x=c" then"`

`(x-a),(x-b)" and "(x-c)" are it's factors"`

`"and "f(x)=k(x-a)(x-b)(x-c)larrcolor(blue)"k is a multiplier"`

`"here "x=-1,x=-2" and "x=3`

`rArr(x+1),(x+2)" and "(x-3)" are the factors"`

`"let "k=1`

`rArrf(x)=(x+1)(x+2)(x-3)`

`color(white)(rArrf(x))=x^3-7x-6larrcolor(blue)"is a possible polynomial"`
graph{x^3-7x-6 [-10, 10, -5, 5]}