Question

How do you write a polynomial equation of least degree given the roots -2, -0.5, 4?

Answer 1

`p(x)=2x^3-3x^2-18x-8`

Explanation:

`"given the roots of a polynomial are"`

`x=a,x=b,x=c,x=d`

`"then the factors of the polynomial are"`

`(x-a),(x-b),(x-c)" and "(x-d)`

`"the polynomial is the the product of the factors"`

`p(x)=(x-a)(x-b)(x-c)(x-d)`

`"here "x=-2,x=-0.5,x=4" are the roots"`

`rArr(x+2),(x+0.5)" and "(x-4)" are the factors"`

`rArrp(x)=(x+2)(x+0.5)(x-4)`

`color(white)(rArrp(x))=2x^3-3x^2-18x-8" possible polynomial"`