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

1 Answer
Sep 22, 2017

Answer:

#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"#