How do you write a polynomial with zeros -2, -4, -7 and leading coefficient 1?
1 Answer
Oct 3, 2016
Explanation:
Given the zeros of a polynomial are
x=a,x=b,x=c Then its factors are
(x-a),(x-b)" and " (x-c) and
y=(x-a)(x-b)(x-c)larr" the polynomial" here the zeros are
x=-2,x=-4" and " x=-7
rArr(x-(-2)),(x-(-4)),(x-(-7)) That is
(x+2),(x+4),(x+7)" are the factors"
y=(x+2)(x+4)(x+7)" is the polynomial" distribute brackets to obtain the polynomial in standard form.
y=(x+2)(x^2+11x+28)
=x^3+11x^2+28x+2x^2+22x+56
y=x^3+13x^2+50x+56larr" is the polynomial"