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

1 Answer
Oct 3, 2016

Answer:

#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"#