Question

Create a polynomial in the form ax^3+bx^2+cx=0 that has solutions of x=0,x=-5 and x=11, where a=3

Answer 1

3x^3-18x^2-165x=0

Since we are given the solutions, we can rewrite them.

x=-5 is (x+5)

x=11 is (x-11)

x=0 is just x

Now we can write our equation:

3x(x+5)(x-11)=0

*3 comes from the a being 3

Now we multiply, I’d recommend starting by using FOIL on the last two first and getting;

3x(x^2-6x-55)=0

Then distribute the 3x:

3x^3-18x^2-165x=0