Well first you have to make the denominators equal by finding a common denominator. in this case 21, but whatever you do to the bottom you do to the top. so 1/3 times 7/7 equals 7/21 and 1/7 times 3/3 equals 3/21.
so how many 7/21 cups of ice cream can you make from 3/21 i think about none but remember i could be wrong
<u>Answer:</u>
The equation of a polynomial of degree 3, with zeros 1, 2 and -1 is ![x^{3}-2 x^{2}-x+2=0](https://tex.z-dn.net/?f=x%5E%7B3%7D-2%20x%5E%7B2%7D-x%2B2%3D0)
<u>Solution:</u>
Given, the polynomial has degree 3 and roots as 1, 2, and -1. And f(0) = 2.
We have to find the equation of the above polynomial.
We know that, general equation of 3rd degree polynomial is
![F(x)=x^{3}-(a+b+c) x^{2}+(a b+b c+a c) x-a b c=0](https://tex.z-dn.net/?f=F%28x%29%3Dx%5E%7B3%7D-%28a%2Bb%2Bc%29%20x%5E%7B2%7D%2B%28a%20b%2Bb%20c%2Ba%20c%29%20x-a%20b%20c%3D0)
where a, b, c are roots of the polynomial.
Here in our problem, a = 1, b = 2, c = -1.
Substitute the above values in f(x)
![F(x)=x^{3}-(1+2+(-1)) x^{2}+(1 \times 2+2(-1)+1(-1)) x-1 \times 2 \times(-1)=0](https://tex.z-dn.net/?f=F%28x%29%3Dx%5E%7B3%7D-%281%2B2%2B%28-1%29%29%20x%5E%7B2%7D%2B%281%20%5Ctimes%202%2B2%28-1%29%2B1%28-1%29%29%20x-1%20%5Ctimes%202%20%5Ctimes%28-1%29%3D0)
![\begin{array}{l}{\rightarrow x^{3}-(3-1) x^{2}+(2-2-1) x-(-2)=0} \\ {\rightarrow x^{3}-(2) x^{2}+(-1) x-(-2)=0} \\ {\rightarrow x^{3}-2 x^{2}-x+2=0}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B%5Crightarrow%20x%5E%7B3%7D-%283-1%29%20x%5E%7B2%7D%2B%282-2-1%29%20x-%28-2%29%3D0%7D%20%5C%5C%20%7B%5Crightarrow%20x%5E%7B3%7D-%282%29%20x%5E%7B2%7D%2B%28-1%29%20x-%28-2%29%3D0%7D%20%5C%5C%20%7B%5Crightarrow%20x%5E%7B3%7D-2%20x%5E%7B2%7D-x%2B2%3D0%7D%5Cend%7Barray%7D)
So, the equation is ![x^{3}-2 x^{2}-x+2=0](https://tex.z-dn.net/?f=x%5E%7B3%7D-2%20x%5E%7B2%7D-x%2B2%3D0)
Let us put x = 0 in f(x) to check whether our answer is correct or not.
![\mathrm{F}(0) \rightarrow 0^{3}-2(0)^{2}-0+2=2](https://tex.z-dn.net/?f=%5Cmathrm%7BF%7D%280%29%20%5Crightarrow%200%5E%7B3%7D-2%280%29%5E%7B2%7D-0%2B2%3D2)
Hence, the equation of the polynomial is ![x^{3}-2 x^{2}-x+2=0](https://tex.z-dn.net/?f=x%5E%7B3%7D-2%20x%5E%7B2%7D-x%2B2%3D0)