Question

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

Answer 1

`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"`