How do you write a polynomial with zeros -2, -4, -7 and leading coefficient 1?

1 Answer
Oct 3, 2016

y=x^3+13x^2+50x+56

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"